EL-5230/EL-5250 04LGK (TINSE0796EHZZ) PRINTED IN CHINA / IMPRIMÉ EN CHINE / IMPRESO EN CHINA PROGRAMMABLE SCIENTIFIC CALCULATOR SHARP CORPORATION ® EL-5230 EL-5250 PROGRAMMABLE SCIENTIFIC CALCULATOR OPERATION MANUAL SHARP EL-5230/5250 Programmable Scientific Calculator Introduction Chapter 1: Before You Get Started Chapter 2: General Information Chapter 3: Scientific Calculations Chapter 4: Statistical Calculations Chapter 5: Equation Solvers Chapter 6: Complex Number Calculations Chapter 7: Programming Chapter 8: Application Examples Appendix 1 Contents Introduction ...........................................................7 Operational Notes .................................................................................... 8 Key Notation in This Manual .................................................................... 9 Chapter 1: Before You Get Started .....................11 Preparing to Use the Calculator ............................................................ 11 Resetting the calculator ................................................................. 11 The Hard Case ....................................................................................... 12 Calculator Layout and Display Symbols ................................................ 13 Operating Modes ................................................................................... 15 Selecting a mode ........................................................................... 15 What you can do in each mode ..................................................... 15 A Quick Tour ........................................................................................... 16 Turning the calculator on and off ................................................... 16 Entering and solving an expression ............................................... 16 Editing an expression ..................................................................... 17 Using variables ............................................................................... 18 Using simulation calculations (ALGB) ........................................... 19 Using the solver function ................................................................ 21 Other features ................................................................................ 22 Chapter 2: General Information .........................23 Clearing the Entry and Memories .......................................................... 23 Memory clear key ........................................................................... 23 Editing and Correcting an Equation ...................................................... 24 Cursor keys .................................................................................... 24 Overwrite mode and insert mode .................................................. 24 Delete key ....................................................................................... 25 Multi-entry recall function ............................................................... 25 The SET UP menu ................................................................................. 26 Determination of the angular unit .................................................. 26 Selecting the display notation and number of decimal places ...... 26 2 Contents Setting the floating point numbers system in scientific notation ... 26 Using Memories ..................................................................................... 27 Using alphabetic characters .......................................................... 27 Using global variables .................................................................... 27 Using local variables ...................................................................... 28 Using variables in an equation or a program ................................. 29 Using the last answer memory ...................................................... 30 Global variable M ........................................................................... 30 Using memory in each mode ......................................................... 31 Resetting the calculator ................................................................. 32 Chapter 3: Scientific Calculations .....................33 NORMAL mode ...................................................................................... 33 Arithmetic operations ..................................................................... 33 Constant calculations ..................................................................... 34 Functions ................................................................................................ 34 Math menu Functions ............................................................................ 36 Differential/Integral Functions ................................................................ 38 Differential function ........................................................................ 38 Integral function .............................................................................. 39 When performing integral calculations .......................................... 40 Random Function .................................................................................. 41 Random numbers ........................................................................... 41 Random dice .................................................................................. 41 Random coin .................................................................................. 41 Random integer .............................................................................. 41 Angular Unit Conversions ...................................................................... 42 Chain Calculations ................................................................................. 42 Fraction Calculations ............................................................................. 43 Binary, Pental, Octal, Decimal and Hexadecimal Operations (N-base) ... 44 Time, Decimal and Sexagesimal Calculations ...................................... 46 Coordinate Conversions ........................................................................ 47 Calculations Using Physical Constants ................................................. 48 Calculations Using Engineering Prefixes .............................................. 50 Modify Function ...................................................................................... 51 3 Contents Solver Function ...................................................................................... 52 Entering and solving an equation .................................................. 52 Changing the value of variables and editing an equation ............. 52 Solving an equation ....................................................................... 53 Important notes .............................................................................. 54 Simulation Calculation (ALGB) .............................................................. 55 Entering an expression for simulation calculation ......................... 55 Changing a value of variables and editing an expression ............. 55 Simulate an equation for different values ...................................... 56 Filing Equations ..................................................................................... 58 Saving an equation ........................................................................ 58 Loading and deleting an equation ................................................. 59 Chapter 4: Statistical Calculations ....................61 Single-variable statistical calculation ............................................. 62 Linear regression calculation ......................................................... 62 Exponential regression, logarithmic regression, power regression, and inverse regression calculation .................. 62 Quadratic regression calculation ................................................... 63 Data Entry and Correction ..................................................................... 63 Data entry ....................................................................................... 63 Data correction ............................................................................... 63 Statistical Calculation Formulas ............................................................ 65 Normal Probability Calculations ............................................................ 66 Statistical Calculations Examples ......................................................... 67 Chapter 5: Equation Solvers ..............................69 Simultaneous Linear Equations ............................................................. 69 Quadratic and Cubic Equation Solvers ................................................. 71 Chapter 6: Complex Number Calculations .......73 Complex Number Entry ......................................................................... 73 Chapter 7: Programming ....................................75 PROG mode ........................................................................................... 75 4 Contents Entering the PROG mode .............................................................. 75 Selecting the NORMAL program mode or the NBASE program mode ................................................................................ 75 Programming concept .................................................................... 75 Keys and display ............................................................................ 76 Creating a NEW Program ...................................................................... 76 Creating a NEW program ............................................................... 76 Use of variables .............................................................................. 77 Programming Commands ...................................................................... 79 Input and display commands ......................................................... 79 Flow control .................................................................................... 81 Equalities and inequalities ............................................................. 82 Statistical Commands ............................................................................ 83 Editing a Program .................................................................................. 84 Error Messages ...................................................................................... 85 Deleting Programs ................................................................................. 86 Chapter 8: Application Examples ......................87 Programming Examples ........................................................................ 87 Some like it hot (Celsius-Fahrenheit conversion) .......................... 87 The Heron Formula ........................................................................ 89 2B or not 2B (N-base conversion) ................................................. 91 T test ............................................................................................... 93 A circle that passes through 3 points ............................................ 95 Radioactive decay .......................................................................... 97 Delta-Y impedance circuit transformation ..................................... 99 Obtaining tensions of strings ....................................................... 102 Purchasing with payment in n-month installments ...................... 104 Digital dice .................................................................................... 106 How many digits can you remember? ......................................... 107 Calculation Examples .......................................................................... 110 Geosynchronous orbits ................................................................ 110 Twinkle, twinkle, little star (Apparent magnitude of stars) ........... 111 Memory calculations .................................................................... 113 The state lottery ........................................................................... 114 5 Contents Appendix ............................................................115 Battery Replacement ........................................................................... 115 Batteries used .............................................................................. 115 Notes on battery replacement ..................................................... 115 When to replace the batteries ...................................................... 115 Cautions ....................................................................................... 116 Replacement procedure ............................................................... 116 Automatic power off function ........................................................ 117 The OPTION menu .............................................................................. 118 The OPTION display .................................................................... 118 Contrast ........................................................................................ 118 Memory check .............................................................................. 118 Deleting equation files and programs .......................................... 119 If an Abnormal Condition Occurs ........................................................ 119 Error Messages .................................................................................... 120 Using the Solver Function Effectively .................................................. 121 Newton’s method .......................................................................... 121 ‘Dead end’ approximations ........................................................... 121 Range of expected values ............................................................ 121 Calculation accuracy .................................................................... 122 Changing the range of expected values ...................................... 122 Equations that are difficult to solve .............................................. 123 Technical Data ..................................................................................... 124 Calculation ranges ....................................................................... 124 Memory usage ............................................................................. 126 Priority levels in calculations ........................................................ 127 Specifications ....................................................................................... 128 For More Information about Scientific Calculators .............................. 129 6 Introduction Thank you for purchasing the SHARP Programmable Scientific Calculator Model EL-5230/5250. After reading this manual, store it in a convenient location for future reference. • Unless the model is specified, all text and other material appearing in this manual applies to both models (EL-5230 and EL-5250). • Either of the models described in this manual may not be available in some countries. • Screen examples shown in this manual may not look exactly the same as what is seen on the product. For instance, screen examples will show only the symbols necessary for explanation of each particular calculation. • All company and/or product names are trademarks and/or registered trademarks of their respective holders. 7 Introduction Operational Notes • Do not carry the calculator around in your back pocket, as it may break when you sit down. The display is made of glass and is particularly fragile. • Keep the calculator away from extreme heat such as on a car dashboard or near a heater, and avoid exposing it to excessively humid or dusty environments. • Since this product is not waterproof, do not use it or store it where fluids, for example water, can splash onto it. Raindrops, water spray, juice, coffee, steam, perspiration, etc. will also cause malfunction. • Clean with a soft, dry cloth. Do not use solvents or a wet cloth. • Do not drop it or apply excessive force. • Never dispose of batteries in a fire. • Keep batteries out of the reach of children. • This product, including accessories, may change due to upgrading without prior notice. NOTICE • SHARP strongly recommends that separate permanent written records be kept of all important data. Data may be lost or altered in virtually any electronic memory product under certain circumstances. Therefore, SHARP assumes no responsibility for data lost or otherwise rendered unusable whether as a result of improper use, repairs, defects, battery replacement, use after the specified battery life has expired, or any other cause. • SHARP will not be liable nor responsible for any incidental or consequential economic or property damage caused by misuse and/ or malfunctions of this product and its peripherals, unless such liability is acknowledged by law. 8 Introduction Key Notation in This Manual In this manual, key operations are described as follows: To specify ex : @ " ..................... 햲 To specify In : i To specify F : ; F ........................... 햳 To specify d/c : @ F ..................... 햲 To specify ab/c : k To specify H : ; H ........................... 햳 To specify i : Q .............................. 햴 햲 Functions that are printed in orange above the key require @ to be pressed first before the key. 햳 When you specify the memory (printed in blue above the key), press ; first. Alpha-numeric characters for input are not shown as keys but as regular alpha-numeric characters. 햴 Functions that are printed in grey (gray) adjacent to the keys are effective in specific modes. Note: • To make the cursor easier to see in diagrams throughout the manual, it is depicted as ‘_’ under the character though it may actually appear as a rectangular cursor on the display. Example Press j @ s ; R A k S 10 • @ s and ; R means you have to press @ followed by ` key and ; followed by 5 key. NORMAL MODE 0. πRŒ˚–10_ 9 10 Chapter 1 Before You Get Started Preparing to Use the Calculator Before using your calculator for the first time, you must reset it and adjust its contrast. Resetting the calculator 1. Press the RESET switch located on the back of the calculator with the tip of a ballpoint pen or similar object. Do not use an object with a breakable or sharp tip. • If you do not see the message on the right, the battery may be installed incorrectly; refer to ‘Battery Replacement’ (See page 115.) and try installing it again. 2. Press y. • The initial display of the NORMAL mode appears. 3. Press @ o 0 and press + or - to adjust the display contrast until it is set correctly, then press j. • @ o means you have to press @ followed by S key. zALL DATA CL?z z YES¬[DEL] z z NO¬[ENTER]z NORMAL MODE 0. LCD CONTRAST [+] [-] DARK® ¬LIGHT • See ‘The OPTION menu’ (See page 118.) for more information regarding optional functions. 11 Chapter 1: Before You Get Started The Hard Case Your calculator comes with a hard case to protect the keyboard and display when the calculator is not in use. Before using the calculator, remove the hard case and slide it onto the back as shown to avoid losing it. When you are not using the calculator, slide the hard case over the keyboard and display as shown. • Firmly slide the hard case all the way to the edge. • The quick reference card is located inside the hard case. • Remove the hard case while holding with fingers placed in the positions shown below. 12 Chapter 1: Before You Get Started Calculator Layout and Display Symbols Calculator layout 1 Display screen 2 Power ON/OFF and Clear key 3 Key operation keys 4 Cursor keys 1 Display screen: The calculator display consists of 14 × 3 line dot matrix display (5 × 7 dots per character) and a 2-digit exponent display per each line. 2 Power ON/OFF and Clear key: Turns calculator ON. To turn off the calculator, press @, then o. This key can also be used to clear the display. 3 Key operation keys: @: Activates the second function (printed in orange) assigned to the next pressed key. ;: Activates the variable (printed in blue) assigned to the next pressed key. 4 Cursor keys: Enables you to move the cursor in four directions. 13 Chapter 1: Before You Get Started Display Symbol Dot matrix display Mantissa Exponent • During actual use, not all symbols are displayed at the same time. • Only the symbols required for the usage under instruction are shown in the display and calculation examples of this manual. : Indicates some contents are hidden in the directions shown. Press cursor keys to see the remaining (hidden) section. BUSY : Appears during the execution of a calculation. 2ndF : Appears when @ is pressed. xy/rθ : Indicates the mode of expression of results in the complex calculation mode. HYP : Indicates that H has been pressed and the hyperbolic functions are enabled. If @ > are pressed, the symbols ‘2ndF HYP’ appear, indicating that inverse hyperbolic functions are enabled. ALPHA: Appears when ;, @ a, x or t is pressed. FIX/SCI/ENG: Indicates the notation used to display a value. DEG/RAD/GRAD: Indicates angular units. : Appears when statistics mode is selected. M 14 : Indicates that a value is stored in the M memory. Chapter 1: Before You Get Started Operating Modes This calculator has five operating modes to perform various operations. These modes are selected from the MODE key. Selecting a mode 1. Press b. The menu display appears. Press d to display the next menu page. <MODE-1> ƒNORMAL ⁄STAT ¤PROG ‹EQN <MODE-2> ›CPLX 2. Press 0 to select the NORMAL mode. • In the menu display, press the assigned number to choose or recall a selection. NORMAL MODE 0. What you can do in each mode NORMAL mode: Allow you to perform standard scientific calculations, Differential/Integral functions, N-base calculations, Solver function, Simulation calculation. STAT (statistics) mode: Allows you to perform statistical calculations. PROG (program) mode: Allows you to create and use programs to automate simple or complex calculations. EQN (equation) mode: Allows you to perform equation solvers, such as quadratic equation. CPLX (complex) mode: Allows you to perform arithmetic operations with complex numbers. 15 Chapter 1: Before You Get Started A Quick Tour This section takes you on a quick tour covering the calculator’s simple arithmetic operations and also principal features like the solver function. Turning the calculator on and off Press j at the top right of the keypad to turn the calculator on. 1. NORMAL MODE 0. • To conserve the batteries, the calculator turns itself off automatically if it is not used for several minutes. Press @ o to turn the calculator off. 2. • Whenever you need to execute a function or command which is written in orange above a key, press @ followed by the key. Entering and solving an expression Arithmetic expressions should be entered in the same order as they would normally be written in. To calculate the result of an expression, press e at the bottom right of the keypad; this has the same function as the ‘equals’ key on some calculators. Example Find the answer to the expression 82 ÷ 았앙 3 – 7 × -10.5 8Az@*3NORMAL MODE 7 k S 10.5 0. • This calculator has a minus key 8Œ©‰3-7˚–10.5_ for subtraction and a negative key S for entering negative numbers. • To correct an error, use the cursor keys l r u d to move to the appropriate position on the display and type over the original expression. 1. 2. Press e to obtain an answer. • While the calculator is computing an answer, BUSY is displayed at the above left of the display. • The cursor does not have to be at the end of an expression for you to obtain an answer. 16 0. 8Œ©‰3-7˚–10.5= 110.4504172 Chapter 1: Before You Get Started Editing an expression After obtaining an answer, you can go back to an expression and modify it using the cursor keys just as you can before the e is pressed. Example Return to the last expression and change it to 82 ÷ 았3 – 7 × -10.5 Press d or r to return to the 8Œ©‰3-7˚–10.5= last expression. 110.4504172 • The cursor is now at the beginning of 8Œ©‰3-7˚–10.5 the expression (on ‘8’ in this case). • Pressing u or l after obtaining an answer returns the cursor to the end of the last expression. • To make the cursor easier to see in diagrams throughout the manual, it is depicted as ‘_’ under the character though it may actually appear as a rectangular cursor on the display. 1. Press r four times to move the cursor to the point where you wish to make a change. • The cursor has moved four places to the right and is now flashing over ‘3’. 2. 8Œ©‰3-7˚–10.5= 110.4504172 8Œ©‰3-7˚–10.5 3. Press @ O . • This changes the character entering mode from ‘overwrite’ to ‘insert’. • When @ is pressed the 2ndF symbol should appear at the above of the display. If it does not, you have not pressed the key firmly enough. • The shape of the flashing cursor tells you which character entering mode you are in. A triangular cursor indicates ‘insert’ mode while a rectangular cursor indicates ‘overwrite’ mode. Press ( and then move the cursor to the end of expression (@ r). • Note that the cursor has moved to the second line since the expression now exceeds 14 characters. 4. 5. Press ) and e to find the answer for the new expression. 110.4504172 8Œ©‰(3-7˚–10.5 8Œ©‰(3-7˚–10.5 )= 7.317272966 17 Chapter 1: Before You Get Started Using variables You can use 27 variables (A-Z and θ) in the NORMAL mode. A number stored as a variable can be recalled either by entering the variable name or using t. Example 1 Store 23 to variable R. 1. Press j 2 1 then x. • j clears the display. • ALPHA appears automatically when you press x. You can now enter any alphabetic character or θ (written in blue above keys in the keypad). 2„Ò_ 2. Press R to store the result of 23 in R. • The stored number is displayed on the next line. • ALPHA disappears from the display. 2„ÒR NORMAL MODE 0. 0. 8. You can also store a number directly rather than storing the result of an expression. Example 2 Find the area of a circle which has radius R. r S = πr 2 Enter an expression containing variable R (now equal to 8) from the last example. 1. Press j @ s then ;. • Whenever you need to use a character written in blue on the keypad, press ; beforehand. ALPHA will appear at the above of the display. 2. Press R and then A. • ALPHA disappears after you have entered a character. 18 NORMAL MODE 0. π_ NORMAL MODE 0. πRŒ_ Chapter 1: Before You Get Started 3. Press e to obtain the result. Follow the same procedure as above, but press t instead of ; in step 1. 0. πRŒ= 201.0619298 You will get the same result. Using simulation calculations (ALGB) If you want to find more than one solution using the same formula or algebraic equation, you can do this quickly and simply by use of the simulation calculation. Example h Find the volume of two cones: 1 with height 10 and radius 8 and 2 with height 8 and radius 9. r V= Press j 1 k 3 @ s ; R A ; H to enter the formula. • Note that ‘1 3’ represents 1 over (i.e. divided by) 3. • Variables can be represented only by capital letters. 1. 1 2 πr h 3 NORMAL MODE 0. 1ı3πRŒH_ Press @ G (I key) to finish 1ı3πRŒH entering the equation. • The calculator automatically picks out H=z 0. the variables alphabetically contained in the equation in alphabetical order and asks you to input numbers for them. • at the bottom of the display reminds you that there is another variable further on in the expression. 2. Press 10 e to input the height and go on the next variable. • The calculator is now asking you to input a number for the next variable. 3. 1ı3πRŒH R=z 8. 19 Chapter 1: Before You Get Started • Note that, as the variable R already has a number stored in memory, the calculator recalls that number. • indicates that there is another variable earlier in the expression. 4. Press 8 to input the radius. Input of all variables is now complete. 5. Press e to obtain the solution. • The answer (volume of cone �) is displayed on the third line. Press e and 8 to input the height for cone �. • The display returns to a value entry screen with ‘8’ substituted for ‘10’ in variable H. 6. 7. Press e to confirm the change. 1ı3πRŒH= 670.2064328 1ı3πRŒH H=8_ 1ı3πRŒH R=z Press 9 to enter the new radius then press e to solve the equation. • The volume of cone � is now displayed. • In any step, press @ h to obtain the solution using the values entered into the variables at that time. 8. 8. 20 1ı3πRŒH= 678.5840132 Chapter 1: Before You Get Started Using the solver function You can solve any unknown variable in an equation by assigning known values to the rest of the variables. Let us compare the differences between the solver function and the simulation calculations using the same expression as in the last example. Example What is the height of cone 3 if it has a radius of 8 and the same volume as cone 2 (r = 9, h = 8) in the last example? h r V= 9. Store the result of step 8 on the previous page in variable V. Press j twice and ; < x V. 10. Input the equation (including ‘=’) in the NORMAL mode. Press ; V ; = then input the rest of the expression. You must press ; = ( m key), not e, to enter the = sign. 11. Press I 5 to move to the variable input display. • Note that the values assigned to the variables in the last example for the simulation calculations are retained and displayed. 12. Press d to skip the height, and then press 8 e to enter the radius (R). • The cursor is now on V. The value that was stored in step 9 is displayed. (volume of cone 2) 13. Press u u to go back to the variable H. • This time the value of H from memory is also displayed. 1 2 πr h 3 0. AnsÒV 678.5840132 AnsÒV 678.5840132 V=1ı3πRŒH_ V=1ı3πRŒH H=z 8. V=1ı3πRŒH V=z678.5840132 V=1ı3πRŒH H=z 8. 21 Chapter 1: Before You Get Started 14. Press @ h to find the height of H= 10.125 cone 3. R¬ 678.5840132 • Note that the calculator finds the L¬ 678.5840132 value of the variable that the cursor is Right and left sides of the on when you press @ h. expression after substituting • Now you have the height of cone 3 the known variables that has the same volume as cone Height of cone 3 2. • R→ and L→ are the values computed by Newton's method, which is used to determine the accuracy of the solution. Other features Your calculator has a range of features that can be used to perform many calculations other than those we went through in the quick tour. Some of the important features are described below. Statistical calculations: You can perform one- and two- variable weighted statistical calculations, regression calculations, and normal probability calculations. Statistical results include mean, sample standard deviation, population standard deviation, sum of data, and sum of squares of data. (See Chapter 4.) Equation solvers: You can perform solvers of simultaneous linear equation with two/three unknowns or quadratic/cubic equation. (See Chapter 5.) Complex number calculations: You can perform addition, subtraction, multiplication, and division calculations. (See Chapter 6.) Programming: You can program your calculator to automate certain calculations. Each program can be used in either the NORMAL or NBASE program modes. (See Chapter 7.) 22 Chapter 2 General Information Clearing the Entry and Memories Operation Entry Local (Display) A- Z, θ*1 variables j Mode selection @P0 @P1y @P2y × × × × × × × Saved equations*2 Multi-entry recall, STAT*4 including saved local variables ANS*3 STAT VAR*5 × × × × × × × × × × *6 × × @P3y RESET switch : Clear *1 *2 *3 *4 *5 *6 × : Retain Global variable memories. Saved equations and local variables by the filing equations function Last answer memory. Statistical data (entered data) n, x¯, sx, σ x, Σ x, Σ x 2, y¯ , sy, σ y, Σ y, Σ y 2, Σ xy, a, b, c, r. Will be cleared when changing between sub-modes in the STAT mode. Note: • To clear one variable memory of global variable and local variable memories, press j x and then choose memory. Memory clear key Press @ P to display the menu. • To initialize the display mode, press 0. The parameters set as follows. • Angular unit: DEG (See page 26.) • Display notation: NORM1 (See page 26.) • N-base: DEC (See page 44.) <M-CLR> ƒDISP ⁄MEMORY ¤STAT ‹RESET • To clear all variables (excluding local variables of saved equations, statistical data and STAT variables), press 1 y. • To clear statistical data and STAT variables, press 2 y. • To RESET the calculator, press 3 y. The RESET operation will erase all data stored in memory and restore the calculator’s default setting. 23 Chapter 2: General Information Editing and Correcting an Equation Cursor keys Incorrect keystrokes can be changed by using the cursor keys (l r u d). Example Enter 123456 then correct it to 123459. 1. Press j 123456. NORMAL MODE 0. 123456_ 2. Press y 9 e. 0. • If the cursor is located at the right end 123459= of an equation, the y key will 123459. function as a backspace key. • You can return to the equation just after getting an answer by pressing the cursor keys. After returning to the equation, the following operations are useful; @ l or @ r: To jump the cursor to the beginning or the end of equation. Overwrite mode and insert mode • Pressing @ O switches between the two editing modes: overwrite mode (default); and insert mode. A rectangular cursor indicates preexisting data will be overwritten as you make entries, while a triangular cursor indicates that an entry will be inserted at the cursor. • In the overwrite mode, data under the cursor will be overwritten by the number you enter. To insert a number in the insert mode, move the cursor to the place immediately after where you wish to insert, then make the desired entry. • The mode set will be retained until @ O is pressed or a RESET operation is performed. 24 Chapter 2: General Information Delete key • To delete a number/function, move the cursor to the number/function you wish to delete, then press y. If the cursor is located at the right end of an equation, the y key will function as a backspace key. Multi-entry recall function Previous equations can be recalled in the NORMAL, STAT or CPLX mode. Up to 160 characters of equations can be stored in memory. When the memory is full, stored equations are deleted in the order of the oldest first. • Pressing @ g will display the previous equation. Further pressing @ g will display preceding equations. • You can edit the equation after recalling it. • The multi-entry memory is cleared by the following operations: mode change, memory clear (@ P 1 y), RESET, N-base conversion. Example Input three expressions and then recall them. 1 3(5+2)= 2 3×5+2= 3 3×5+3×2= 1. Press j 3 ( 5 + 2 ) e 3k 5+2e 17. 3˚5+3˚2= 21. 3k 5+3k2e 2. Press @ g to recall the expression 3. 3˚5+3˚2= 21. 3˚5+3˚2 3. Press @ g to recall the expression 2. 3˚5+3˚2= 21. 3˚5+2 4. Press @ g to recall the expression 1. 3˚5+3˚2= 21. 3(5+2) 25 Chapter 2: General Information The SET UP menu The SET UP menu enables you to change the angular unit and the display format. • Press @ J to display the SET UP menu. • Press j to exit the SET UP menu. <SET UP> ƒDRG ⁄FSE ¤--- Determination of the angular unit The following three angular units (degrees, radians, and grads) can be specified. • DEG(°) : Press @ J 0 0 • RAD (rad): Press @ J 0 1 • GRAD (g) : Press @ J 0 2 Selecting the display notation and number of decimal places Five display notation systems are used to display calculation results: Two settings of Floating point (NORM1 and NORM2), Fixed decimal point (FIX), Scientific notation (SCI) and Engineering notation (ENG). • When @ J 1 0 (FIX) or @ J 1 2 (ENG) is pressed, ‘TAB(0-9)?’ will be displayed and the number of decimal places (TAB) can be set to any value between 0 and 9. • When @ J 1 1 (SCI) is pressed, ‘SIG(0-9)?’ will be displayed and the number of significant digits (SIG) can be set to any value between 0 and 9. Entering 0 will set a 10-digit display. • When a floating point number does not fit in the specified range, the calculator will display the result using the scientific notation (exponential notation) system. See the next section for details. Setting the floating point numbers system in scientific notation The calculator has two settings for displaying a floating point number: NORM1 (default setting) and NORM2. In each display setting, a number is automatically displayed in scientific notation outside a preset range: • NORM1: 0.000000001 ≤ |x| ≤ 9999999999 • NORM2: 0.01 ≤ |x| ≤ 9999999999 26 Chapter 2: General Information Example 100000÷3= [Floating point (NORM1)] →[FIXed decimal point and TAB set to 2] →[SCIentific notation and SIG set to 3 ] →[ENGineering notation and TAB set to 2] →[Floating point (NORM1)] 3÷1000= [Floating point (NORM1)] →[Floating point (NORM2)] →[Floating point (NORM1)] Key operations Result j@J13 100000 z 3 e @J102 33333.33333 33333.33 04 @J113 3.33˚10 @J122 33.33˚10 @J13 03 33333.33333 j 3 z 1000 e @J14 @J13 0.003 -03 3.˚10 0.003 Using Memories The calculator uses global variable memories (A–Z and θ), local variable memories (maximum of nine variables per equation), and a last answer memory used when solving equations. Using alphabetic characters You can enter an alphabetic character (written in blue) when ALPHA is displayed at the top of the display. To enter this mode, press ;. To enter more than one alphabetic character, press @ a to apply the alphabet-lock mode. Press ; to escape from this mode. NORMAL MODE 0. Using global variables You can assign values (numbers) to global variables by pressing x then A–Z and θ. Example 1 Store 6 in global variable A. 1. Press j 6 x A. • There is no need to press ; because ALPHA is selected automatically when you press x. 0. 6ÒA 6. 27 Chapter 2: General Information Example 2 Recall global variable A. 1. Press t A. • There is no need to press ; because ALPHA is selected automatically when you press t. 6. A= 6. Using local variables Nine local variables can be used in each equation or program, in addition to the global variables. Unlike global variables, the values of the local variables will be stored with the equation when you save it using the filing equations function. (See page 58.) To use local variables, you first have to assign the name of the local variable using two characters: the first character must be a letter from A to Z or θ and the second must be a number from 0 to 9. Example Store 1.25 x 10-5 as local variable A1 (in the NORMAL mode) and recall the stored number. 1. Press @ v. • The VAR menu appears. • If no local variables are stored yet, ALPHA appears automatically and the calculator is ready to enter a name. 2. Press A1 e. • ¬ shows that you have finished assigning the name A1. • To assign more names, press d to move the cursor to VAR 1 and repeat the process above. ƒz ⁄ ¤ ‹ › ﬁ ﬂ ‡ ° ¬ƒA¡ ‹ ⁄ › ¤ ﬁ ﬂ ‡ ° 3. Press j. • This returns you to the previous screen. 4. 28 Press 1.25 ` S 5 x @ v 0. 0. 1.25E–5ÒA1 0.0000125 Chapter 2: General Information • You do not need to enter an alphabetic character. Just specify the named local variable using a number from 0 to 8, or move the arrow to the appropriate variable the press e. 5. Press @ v 0 e. • The value of VAR 0 will be recalled. • Alternatively you can recall a variable by moving the arrow to it then press e twice. 0.0000125 A1= 0.0000125 Note: • You can change the name of a local variable by overwriting it in the VAR menu. The cursor appears when r is pressed in the VAR menu. • Local variables not stored using the filing equations function will be deleted by mode selection or memory clear operation (@ P 1 y). • Local and global variables will be cleared by creating a new program, and editing and running a program. Using variables in an equation or a program Both global and local variables can be used directly in an equation or a program. Local variables are useful when you need to use variables such as X1 and X2 at the same time in another equation. The local variable names and their values can be saved in each equation. (See page 58.) Example Using A (6) and A1 (0.0000125) from the last two examples, solve the expression. 1 — – 1000A A1 1. Press j 1 k. • Start entering the expression. NORMAL MODE 0. 1ı_ 2. Press @ v. 3. Press 0 - 1000 ; A e. • The display returns automatically to the previous screen after you have chosen the local variable, and you can continue to enter the expression. • You do not need k if you use a variable. However, the variable must be a multiplier. ¬ƒA¡ ‹ ⁄ › ¤ ﬁ ﬂ ‡ ° 0. 1ıA¡-1000A= 74000. 29 Chapter 2: General Information Using the last answer memory The calculator always keeps the most recent answer in ANS memory and replaces it with the new answer every time you press an ending instruction (e, x etc.). You may recall the last answer and use it in the next equation. Example Evaluate the base area (S = 32π) and volume of a cylinder (V = 5S) using the last answer memory. h=5 r=3 1. Press j 3 A @ s e. • The area of the base is now calculated. • The number 28.27433388 is held in ANS memory. 0. 3Œπ= 28.27433388 2. Press j 5 ; < e. • You now have the volume of the cylinder. 0. 5Ans= 141.3716694 The last answer is cleared (i.e. set to 0) if you press the RESET switch, change the mode or memory clear operation (@ P 1 y), but not if you turn the calculator off. Global variable M Using the M memory, in addition to the features of global variables, a value can be added to or subtracted from an existing memory value. Example $150×3:Ma +)$250:Mb=Ma+250 –)Mb×5% M Key operations jxM 150 k 3 m 250 m t Mk 5@ % @MtM • m and @ M cannot be used in the STAT mode. 30 Result 0. 450. 250. 35. 665. Chapter 2: General Information Using memory in each mode Mode ANS M A-L, N-Z, Local variables NORMAL STAT PROG EQN CPLX : Available : Unavailable Notes: • Calculation results from the functions indicated below are automatically stored in memories replacing any existing values. • →r θ, →xy.................. R memory (r) θ memory (θ) X memory (x) Y memory (y) • Use of t or ; will recall the value stored in memory using up to 14 digits in accuracy. 31 Chapter 2: General Information Resetting the calculator If you wish to clear all memories, variables, files and data, or if none of the keys (including j) will function, press the RESET switch located on the back of the calculator. In rare cases, all the keys may cease to function if the calculator is subjected to strong electrical noise or heavy shock during use. Follow the instructions below to reset the calculator. Caution: • The RESET operation will erase all data stored in memory and restore the calculator's default setting. 1. Press the RESET switch located on the back of the calculator with the tip of a ballpoint pen or similar object. Do not use an object with a breakable or sharp tip. • A display appears asking you to confirm that you really want to reset the calculator. Press y. 2. • All memories, variables, files and data are cleared. • The display goes back to the initial display in the NORMAL mode. • The calculator will revert to the very first settings that were made when you started to use the calculator for the first time. zALL DATA CL?z z YES¬[DEL] z z NO¬[ENTER]z z ALL DATA z z CLEARED! z z z NORMAL MODE 0. Or, to cancel the operation, press e. Note: • When corruption of data occurs, the reset procedure may automatically be initiated upon pressing the RESET switch. • Pressing @ P and 3 y can also clear all memories, variables, files and data as described above. 32 Chapter 3 Scientific Calculations NORMAL mode NORMAL mode is used for standard scientific calculations, and has the widest variety of functions. Many of the functions described in this chapter are also available for use in other modes. Press b 0 to select the NORMAL mode. • Differential/Integral functions, N-base functions, Solver functions and Simulation Calculation (ALGB) in this chapter are all performed in the NORMAL mode. • In each example of this chapter, press j to clear the display first. If the FIX, SCI or ENG indicator is displayed, clear the indicator by selecting ‘NORM1’ from the SET UP menu. Unless specified, set the angular unit as ‘DEG’. (@ P 0) Arithmetic operations Example Key operations 45+285÷3= j 45 + 285 z 3 e 18+6 = 15–8 ( 18 + 6 ) z ( 15 - 8 ) e 42×(–5)+120= 42 k S 5 + 120 e 3 –3 (5×10 )÷(4×10 )= 5` 3z 4` S 3e Result 140. 3.428571429 –90. 1250000. 33 Chapter 3: Scientific Calculations Constant calculations Example Key operations Result 34+57= 34 + 57 e 91. 45+57= 45 e 102. 68×25= 68 k 25 e 1700. 68×40= 40 e 2720. • In constant calculations, the addend becomes a constant. Subtraction and division behave the same way. For multiplication, the multiplicand becomes a constant. • In constant calculations, constants will be displayed as ∆. Functions Example Key operations Result sin60 [°]= j v 60 e 0.866025403 π cos — [rad]= 4 @J01$ @ s k 4e 0.707106781 –1 tan 1 [g]= @J02@y1 e @P0 50. • The range of the results of inverse trigonometric functions DEG RAD GRAD 34 θ = sin–1 x, θ= tan–1 x θ = cos–1 x –90 ≤ θ ≤ 90 0 ≤ θ ≤ 180 π π — –— 2 ≤θ≤ 2 –100 ≤ θ ≤ 100 0 ≤θ≤π 0 ≤ θ ≤ 200 Chapter 3: Scientific Calculations Example Key operations Result (cosh 1.5 + sinh 1.5)2 = j ( H $ 1.5 + H v 1.5 ) A e 20.08553692 5 tanh–1— = 7 @>t(5 z 7) e 0.895879734 ln 20 = i 20 e 2.995732274 log 50 = l 50 e 1.698970004 e3 = @ " 3e 20.08553692 101.7 = @ Y 1.7 e 50.11872336 1 1 —+—= 6 7 6 @ Z + 7@ Ze 0.309523809 8 –3 ×5 = –2 4 2 8m S 2- 3m 4k 5A e 4= (123)— 12 m 3 m 4 @Ze 83 = 81 e 1 49 – 3 4 81 = 27 = 4! = -2024.984375 6.447419591 512. @ * 49 - 4 @ D 81 e 4. @ q 27 e 3. 4@ B e 24. P3 = 10 @ e 3 e 720. 5 C2 = 5@ c 2e 10. 500×25%= 500 k 25 @ % 125. 120÷400=?% 120 z 400 @ % 30. 500+(500×25%)= 500 + 25 @ % 625. 400–(400×30%)= 400 - 30 @ % 280. 10 35 Chapter 3: Scientific Calculations Math menu Functions Other functions are available on this calculator besides the first and second functions on the key pad. These functions are accessed using the math function menu. The math menu has different contents for each mode. Press I to display the math menu. In the NORMAL mode, you can recall the following functions. <MATH MENU-1> ƒabs ⁄ipart ¤int ‹fpart → <MATH MENU-2> d ›ÒRAND ﬁSOLVE ﬂΩsec ‡Ωmin • Switch the display using d u. • These math menus are not available for Differential/Integral functions, N-base functions, Solver functions and Simulation Calculation (ALGB). Function Key operations Result 0: abs Displays the absolute value of a number. I0S 7e abs–7= 1: ipart Displays the integer part only of a number. I1S 7.94 e ipart–7.94= –7. 2: int Displays the largest integer less than or equal to a number. I2S 7.94 e int–7.94= 3: fpart Displays the fractional part only of a number. I3S 7.94 e fpart–7.94= –0.94 4: ⇒RAND Before using the Random Numbers 0.001 I 4 of Random functions, designate 0.001 from 0.999 random number sequences available. The calculator can regenerate the same random numbers from the @w0 beginning. e If you wish to go back to normal random numbers, press 0 I 4. 36 7. –8. 0.001ÒRAND 0.001 random= 0.232 Chapter 3: Scientific Calculations Function 5: SOLVE Enter the Solver function mode. (See page 52.) Key operations I 5 Result 6: Ωsec Sexagesimal numbers are converted to seconds notation. (See page 46.) 24 [ I 6 24∂Ωsec 7: Ωmin Sexagesimal numbers are converted to minutes notation. (See page 46.) 0[0[ 1500 I 7 0∂0∂1500Ωmin 25. 86400. 37 Chapter 3: Scientific Calculations Differential/Integral Functions Differential and integral calculations can only be performed in the NORMAL mode. It is possible to reuse the same equation over and over again and to recalculate by only changing the values without having to re-enter the equation. • • • • Performing a calculation will clear the value in the X memory. You can use both global and local variables in the equation. The answer calculated will be stored in the last answer memory. The answer calculated may include a margin of error, or an error may occur. In such a case, recalculate after changing the minute interval (dx) or subinterval (n). • Since differential and integral calculations are performed based on the following equations, in certain rare cases correct results may not be obtained, such as when performing special calculations that contain discontinuous points. Integral calculation (Simpson’s rule): 1 S=—h{f (a)+4{f (a+h)+f (a+3h)+······+f (a+(N–1)h)} 3 +2{f (a+2h)+f (a+4h)+······+f (a+(N–2)h)}+f(b)} b–a h= —— N N=2n a ≤x≤ b Differential calculation: dx dx f(x+ ––)–f(x– ––) 2 2 f’(x)=———————— dx Differential function The differential function is used as follows. 1. Press b 0 to enter the NORMAL mode. 2. Input a formula with an x variable. 3. Press @ 3. 4. Input the x value and press e. 5. Input the minute interval (dx). 6. Press e to calculate. 38 Chapter 3: Scientific Calculations • To exit the differential function, press j. • After getting the answer, press e to return to the display for inputting the x value and the minute interval, and press @ h to recalculate at any point. Example Key operations d/dx (x4–0.5x3+6x2) j ; X* m 4 - 0.5 ;X1+6; XA@3 x=2 dx = 0.00002 d/dx = ? 2ee x=3 dx = 0.001 d/dx = ? e 3 e 0.001 e Result ≈^4-0.5≈„+6≈Œ 0. ≈=z dx: 0.00001 ≈^4-0.5≈„+6≈Œ d/dx= 50. ≈^4-0.5≈„+6≈Œ d/dx= 130.5000029 * X memory is specified by pressing ; then the 3 key. Integral function The Integral function is used as follows. 1. Press b 0 to enter the NORMAL mode. 2. Input a formula with an x variable. 3. Press {. 4. Input the starting value (a) of a range of integral and press e. 5. Input the finishing value (b) of a range of integral and press e. 6. Input the subinterval (n). 7. Press e to calculate. • To exit the integral function, press j. • After getting the answer, press e to return to the display for inputting a range of integral and subinterval, and press @ h to recalculate at any point. 39 Chapter 3: Scientific Calculations Example 8 Key operations Result ∫ 2 (x2–5)dx j;XA-5 { a=z b= n= n = 100 ∫ dx = ? 2e8ee ≈Œ-5 ∫dx= n = 10 ∫ dx = ? e e e 10 e 0. 0. 100. 138. ≈Œ-5 ∫dx= 138. When performing integral calculations Integral calculations require a long calculation time, depending on the integrands and subintervals input. During calculation, ‘calculating!’ will be displayed. To cancel calculation, press j. Note that there will be greater integral errors when there are large fluctuations in the integral values during minute shifting of the integral range and for periodic functions, etc., where positive and negative integral values exist depending on the interval. For the former case, make the integral interval as small as possible. For the latter case, separate the positive and negative values. Following these tips will provide calculations results with greater accuracy and will also shorten the calculation time. y x0 y x2 b a 40 x0 x 1 x2 x3 bx a x x1 x3 Chapter 3: Scientific Calculations Random Function The Random function has four settings for the NORMAL, STAT or PROG mode. (This function is not available while using the N-base function, solver function and simulation calculations.) Random numbers A pseudo-random number, with three significant digits from 0 up to 0.999, can be generated by pressing @ w 0 e. To generate further random numbers in succession, press e. Press j to exit. • The calculator can regenerate the same random number. (See page 36.) Random dice To simulate a die-rolling, a random integer between 1 and 6 can be generated by pressing @ w 1 e. To generate further random numbers in succession, press e. Press j to exit. Random coin To simulate a coin flip, 0 (head) or 1 (tail) can be randomly generated by pressing @ w 2 e. To generate further random numbers in succession, press e. Press j to exit. Random integer An integer between 0 and 99 can be generated randomly by pressing @ w 3 e. To generate further random numbers in succession, press e. Press j to exit. Example Pick a random number between 0 and 9.99. Key operations j@w0 k 10 e Result 0. random˚10= 6.31 • The result may not be the same each time this operation is performed. 41 Chapter 3: Scientific Calculations Angular Unit Conversions The angular unit is changed in sequence each time @ ] ( . key) is pressed. Example Key operations Result 90°→ [rad] → [g] → [°] j 90 @ ] @] @] 1.570796327 100. 90. sin–10.8 = [°] → [rad] → [g] → [°] @ w 0.8 e @] @] @] 53.13010235 0.927295218 59.03344706 53.13010235 Chain Calculations The previous calculation result can be used in a subsequent calculation. However, it cannot be recalled after entering multiple instructions. • When using postfix functions ( , sin, etc.), a chain calculation is possible even if the previous calculation result is cleared by the use of the j key. Example Key operations 6+4=ANS ANS+5 j6+4e +5e 8×2=ANS ANS2 8k2e Ae 44+37=ANS ANS= 44 + 37 e @*e 42 Result 10. 15. 16. 256. 81. 9. Chapter 3: Scientific Calculations Fraction Calculations Arithmetic operations and memory calculations can be performed using fractions, and conversions between decimal numbers and fractions. • If the number of digits to be displayed is greater than 10, the number is converted to and displayed as a decimal number. Example 1 4 b 3— + — = [a—] c 2 3 →[a.xxx] →[d/c] 2 — 10 3 = 5 (—75 ) = 1 — 3 (—18 ) Key operations Result j3k1k2+ 4k3e k @F 4ı5ı6 * 4.833333333 29ı6 @Y2k3e 4.641588834 7k5m5e 16807ı3125 1k8m1k3e 1ı2 @ * 64 k 225 e 8ı15 23 —= 34 (2m3)k (3m4)e 8ı81 1.2 —– = 2.3 1.2 k 2.3 e 1°2’3” ——– = 2 1[2[3k2e 0∂31∂1.5∂ 1×103 ——– = 2×103 1`3k2`3e 1ı2 = 64 —— = 225 A=7 4 —= A 2 1.25 + — = [a.xxx] 5 b →[a—] c 5 * 4ı5ı6 = 4— 6 j7xA 4k;Ae 1.25 + 2 k 5 e k 12ı23 7. 4ı7 1.65 1ı13ı20 43 Chapter 3: Scientific Calculations Binary, Pental, Octal, Decimal, and Hexadecimal Operations (N-base) This calculator can perform conversions between numbers expressed in binary, pental, octal, decimal and hexadecimal systems. It can also perform the four basic arithmetic operations, calculations with parentheses and memory calculations using binary, pental, octal, decimal, and hexadecimal numbers. Furthermore, the calculator can carry out the logical operations AND, OR, NOT, NEG, XOR and XNOR on binary, pental, octal and hexadecimal numbers. Conversion to each system is performed by the following keys: @ z: Converts to the binary system. ‘?’ appears. @ r: Converts to the pental system. ‘q’ appears. @ g: Converts to the octal system. ‘f’ appears. @ h: Converts to the hexadecimal system. ‘6’ appears. @ /: Converts to the decimal system. ‘?’, ‘q’, ‘f’ and ‘6’ disappear from the display. Conversion is performed on the displayed value when these keys are pressed. Note: Hexadecimal numbers A – F are entered into the calculator by pressing ,, m, A, 1, l, and i key respectively. In the binary, pental, octal, and hexadecimal systems, fractional parts cannot be entered. When a decimal number having a fractional part is converted into a binary, pental, octal, or hexadecimal number, the fractional part will be truncated. Likewise, when the result of a binary, pental, octal, or hexadecimal calculation includes a fractional part, the fractional part will be truncated. In the binary, pental, octal, and hexadecimal systems, negative numbers are displayed as a complement. 44 Chapter 3: Scientific Calculations Example Key operations Result DEC(25)→BIN j @ / 25 @ z HEX(1AC) →BIN →PEN →OCT →DEC @ a 1AC @z @r @g @/ BIN(1010–100) ×11 = @ z ( 1010 - 100 ) k 11 e BIN(111)→NEG d 111 e HEX(1FF)+ OCT(512)= HEX(?) @ a 1FF @ g + 512 e @a 2FEC– 2C9E=(A) +)2000– 1901=(B) (C) j x M @ a 2FEC - 2C9Em 2000 1901 m tM 1011 AND 101 = (BIN) j @ z 1011 4 101 e 1.b 5A OR C3 = (HEX) @ a 5A p C3 e DB.H NOT 10110 = (BIN) @ z n 10110 e 1111101001.b 24 XOR 4 = (OCT) @ g 24 x 4 e B3 XNOR 2D = (HEX) →DEC @ a B3 C 2D e @/ 11001.b 110101100.b 3203.P 654.0 428. 10010.b 1111111001.b 1511.0 349.H 34E.H 6FF.H A4D.H 20.0 FFFFFFFF61.H –159. 45 Chapter 3: Scientific Calculations Time, Decimal and Sexagesimal Calculations Conversion between decimal and sexagesimal numbers can be performed, and, while using sexagesimal numbers, also conversion to seconds and minutes notation. The four basic arithmetic operations and memory calculations can be performed using the sexagesimal system. Notation for sexagesimal is as follows: 12∂34∂56.78∂ degree Example minute second Key operations 12°39’18.05” →[10] j 12 [ 39 [ 18.05 @: 123.678→[60] 123.678 @ : 3h30m45s + 6h45m36s = [60] 3 [ 30 [ 45 + 6 [ 45 [ 36 e 1234°56’12” + 0°0’34.567” = [60] 1234 [ 56 [ 12 + 0 [ 0 [ 34.567 e 3h45m – 1.69h = [60] 3 [ 45 - 1.69 e @: sin62°12’24” = [10] v 62 [ 12 [ 24 e 24°→[ ” ] 24 [ I 6 1500”→[ ’ ] 0 [ 0 [ 1500 I 7 46 Result 12.65501389 123∂40∂40.8∂ 10∂16∂21.∂ 1234∂56∂47.∂ 2∂3∂36.∂ 0.884635235 86400. 25. Chapter 3: Scientific Calculations Coordinate Conversions Conversions can be performed between rectangular and polar coordinates. Y P (x, y) Y r P (r, θ) y 0 x X Rectangular coordinate 0 θ X Polar coordinate • Before performing a calculation, select the angular unit. • The calculation result is automatically stored in memories. • Value of r: R memory • Value of θ: θ memory • Value of x: X memory • Value of y: Y memory • r and x values are stored in the last answer memory. Example Key operations Result x=6 r= → θ = [°] y=4 j6,4 @u r= 7.211102551 = 33.69006753 r = 14 14 , 36 @E x= 11.32623792 y= 8.228993532 θ = 36[°] → x= y= 47 Chapter 3: Scientific Calculations Calculations Using Physical Constants Recall a constant by pressing @ c followed by the number of the physical constant designated by a 2-digit number. The recalled constant appears in the display mode selected with the designated number of decimal places. Physical constants can be recalled in the NORMAL mode (when not set to binary, pental, octal, or hexadecimal), STAT mode, PROG mode and EQN mode. Note: Physical constants are based either on the 2002 CODATA recommended values, or the 1995 Edition of the ‘Guide for the Use of the International System of Units (SI)’ released by NIST (National Institute of Standards and Technology), or on ISO specifications. No. 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 48 Constant Speed of light in vacuum Newtonian constant of gravitation Standard acceleration of gravity Electron mass Proton mass Neutron mass Muon mass Atomic mass unit-kilogram relationship Elementary charge Planck constant Boltzmann constant Magnetic constant Electric constant Classical electron radius Fine-structure constant Bohr radius Rydberg constant Magnetic flux quantum Bohr magneton Electron magnetic moment Nuclear magneton Proton magnetic moment Neutron magnetic moment Symbol c, c 0 G gn me mp mn mµ lu e h k µ0 ε0 re α a0 R∞ Φ0 µB µe µN µp µn Unit m s–1 m3 kg–1 s–2 m s–2 kg kg kg kg kg C Js J K–1 N A–2 F m–1 m m m–1 Wb J T–1 J T–1 J T–1 J T–1 J T–1 Chapter 3: Scientific Calculations No. 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 Constant Symbol Muon magnetic moment Compton wavelength Proton Compton wavelength Stefan-Boltzmann constant Avogadro constant Molar volume of ideal gas (273.15 K, 101.325 kPa) Molar gas constant Faraday constant Von Klitzing constant Electron charge to mass quotient Quantum of circulation Proton gyromagnetic ratio Josephson constant Electron volt Celsius Temperature Astronomical unit Parsec Molar mass of carbon-12 Planck constant over 2 pi Hartree energy Conductance quantum Inverse fine-structure constant Proton-electron mass ratio Molar mass constant Neutron Compton wavelength First radiation constant Second radiation constant Characteristic impedance of vacuum Standard atmosphere Example V0 = 15.3 m/s t = 10 s 1 2 V0 t + gt = ? m 2 µµ Unit –1 λc λc, p σ NΑ, L JT m m W m–2 K–4 mol–1 Vm m3 mol–1 R F RK -e/me h/2me γp KJ eV t AU pc M(12C) -h J mol–1 K–1 C mol–1 Ohm C kg–1 m2 s–1 s –1 T–1 Hz V–1 J K m m kg mol–1 Eh Js J G0 s mp/me Mu kg mol–1 λc, n c1 c2 m W m2 mK α –1 Z0 Key operations j 15.3 k 10 + 2 @ Z k @ c 03 k 10 Ae Ω Pa Result 643.3325 49 Chapter 3: Scientific Calculations Calculations Using Engineering Prefixes Calculation can be executed in the NORMAL mode (excluding N-base), STAT mode and PROG mode using the following 12 types of prefixes. Prefix E P T G M k m µ n p f a (Exa) (Peta) (Tera) (Giga) (Mega) (kilo) (milli) (micro) (nano) (pico) (femto) (atto) Example 100m × 10k = 50 Operation @j0 @j1 @j2 @j3 @j4 @j5 @j6 @j7 @j8 @j9 @jA @jB Key operations 100 @ j 6 k 10 @ j 5 e Unit 1018 1015 1012 109 106 103 10–3 10–6 10–9 10–12 10–15 10–18 Result 1000. Chapter 3: Scientific Calculations Modify Function Calculation results are internally obtained in scientific notation with up to 14 digits for the mantissa. However, since calculation results are displayed in the form designated by the display notation and the number of decimal places indicated, the internal calculation result may differ from that shown in the display. By using the modify function, the internal value is converted to match that of the display, so that the displayed value can be used without change in subsequent operations. Example 5÷9=ANS ANS×9= [FIX,TAB=1] Key operations j@J101 5z9e k 9 e*1 5z9e@n k 9 e*2 @P0 Result 0.6 5.0 0.6 5.4 *1 5.5555555555555×10–1×9 *2 0.6×9 51 Chapter 3: Scientific Calculations Solver Function This function enables you to find any variable in an equation. Entering and solving an equation The solver function is used as follows. 1. Press b 0 to enter the NORMAL mode. 2. Enter both sides of an equation, using ‘=’ and variable names. 3. Press I 5. 4. Enter the value of the known variables. 5. Move the cursor (display) to the unknown variables. Press @ h. 6. • The solver function can find any variable anywhere in an equation. It can even find variables that appear several times in an equation. • You can use both global and local variables in your equation. (See page 58.) NORMAL MODE 0. TŒ=(4π©GM)R_ Equation entering display • Using the solver function will cause variables memory to be overwritten with new values. • To exit the solver function, press j. Changing the value of variables and editing an equation When you are in the solution display, press e to return to the display for entering values of variables, then return to the equation display in the NORMAL mode by pressing j. R= 1.127251652 R¬ 9. L¬ 9. Solution display 52 TŒ=(4π©GM)R → e G=z 1.5 Use d u to move between variables. NORMAL MODE 0. → j TŒ=(4π©GM)R_ Chapter 3: Scientific Calculations Solving an equation Example Try finding the variables in the equation below. A×B = C × D 1. Press b 0 to select the NORMAL mode. Press ; A k ; B ; = ; C k ; D. • You must enter the whole equation. 2. NORMAL MODE 0. A˚B=C˚D_ 3. Press I 5. • The calculator automatically calls the A˚B=C˚D display for entering variables and displays the variables in alphabetical A=z 0. order. • indicates that there are more variables. • If a variable already has a value, the calculator displays that value automatically. 4. Press 10 e. • Enters a value for known variable A. • The cursor moves onto the next variable. 5. Press 5 e. • Enters a value for known variable B. A˚B=C˚D B=z A˚B=C˚D C=z 6. Press 2.5 e. • Enters a value for known variable C. • The cursor moves onto the next variable. indicates that this is the last variable. 7. Press @ h. • After showing the ‘calculating!’ display, the calculator finds the value for the unknown variable that was indicated by the cursor. 0. 0. A˚B=C˚D D=z 0. D= R¬ L¬ 20. 50. 50. Values of the left-hand side of the equation Values of the right-hand side of the equation 53 Chapter 3: Scientific Calculations • The value shown on the display for the unknown variable does not have to be set to 0 to solve the equation. • The answer is displayed on the top line and the values of the lefthand and right-hand sides of the equation appear below. 8. Press e. • Returns you to the display for entering variables. 9. Press d 8 e. • Substitutes the value 8 for B. • The cursor moves onto the next variable C. 10. Press @ h. • You can find any unknowns in the same equation. A˚B=C˚D A=z 10. A˚B=C˚D C=z 2.5 C= R¬ L¬ 4. 80. 80. Important notes There are several important points to remember when you use the solver function. • To cancel calculation, press j when ‘calculating!’ is displayed. • Before entering the equation, the appropriate angular unit must be selected. • The calculator uses Newton’s method to solve equations. Due to this, there may be some equations that it fails to solve even though they are in fact solvable. (See page 123.) • The calculator stops calculating when the values it has obtained for the left and right sides of the equation become very close. Thus in certain cases the solution it gives may not be the real answer. (See page 122.) • In certain cases, the calculator may abort a calculation and display the message shown on the right. (See page - ERROR 02 121.) CALCULATION 54 Chapter 3: Scientific Calculations Simulation Calculation (ALGB) This function enables you to find different solutions quickly using different sets of values in the same expression. Entering an expression for simulation calculation The simulation calculation is used as follows. 1. Press b 0 to enter the NORMAL mode. 2. Enter an expression with at least one variable. 3. Press @ G. 4. Enter the values of the variables. The calculation result will be displayed after entering the value for all used variables. • You can use both global and local variables in your equation, but only local variables will be stored if you save the equation. (See page 58.) • You need enter only the side of the equation that contains the variables. • Performing simulation calculation will cause the variables memories to be overwritten with new values. • The answer calculated will be stored in last answer memory. • To exit simulation calculation, press j. Changing a value of variables and editing an expression When you are in the solution display, press e to return to the display for entering values of variables, then return to the equation display in the NORMAL mode by pressing j. πRŒH= 785.3981634 Solution display πRŒH → e H=z NORMAL MODE 5. → j πRŒH_ 0. Use d u to move between variables. 55 Chapter 3: Scientific Calculations Simulate an equation for different values Example Find the area S = bc sin A ÷ 2 when: A 1 b = 3, c = 5 and A = 90° (DEG) 2 b = 3, c = 5 and A = 45° (DEG) 3 b = 4, c = 5 and A = 45° (DEG) 1. S Press b 0 to select the NORMAL mode. 2. Press @ J 0 0 j. • Sets the angular unit to DEG. Press ; B ; C v ; A z 2. • The equation is entered in the normal way. 3. 4. Press @ G. • The calculator automatically calls the display for entering variables and picks out the variables in alphabetical order. • If a variable already has a value, the calculator displays that value automatically. • indicates that there are more variables. 5. Press 90 e. • The calculator picks out the next variable. 6. • Press 3 e 5. indicates that this is the last variable. c b S = bc sin A ÷ 2 NORMAL MODE 0. BCsinA©2_ BCsinA©2 A=z 0. BCsinA©2 B=z 0. BCsinA©2 C=5_ 7. Press e. BCsinA©2= 7.5 Area of triangle 1 is 7.5 square units. 56 Chapter 3: Scientific Calculations 8. Press e and then 45 e. • After getting the answer, press e to return to the display for entering variables. 9. Press @ h. • Sides b and c are both the same length in triangle 2 as in triangle 1, so you do not have to re-enter these values. 2BCsinA©2 B=z 3. BCsinA©2= 5.303300859 Area of triangle 2 is displayed. 10. Press e and then d 4 e @ h. BCsinA©2= 7.071067812 Area of triangle 3 is displayed. 57 Chapter 3: Scientific Calculations Filing Equations When the calculator is in the NORMAL mode (excluding N-base), you can save equations in the EQUATION FILE. Saved equations can be loaded or deleted in the NORMAL mode. Press f in the NORMAL mode to call the EQUATION FILE menu. • Press 0, 1 or 2 to select if an equation is to be loaded, saved or deleted, respectively. <EQTN FILE> ƒLOAD ⁄SAVE ¤DEL Saving an equation You can save an equation as follows. 1. After entering an equation in the NORMAL mode, press 1 in the EQUATION FILE menu. SAVE:TITLE? • The file name display appears asking you to enter a title. • The calculator automatically locks ALPHA on to enable you to enter alphabetic characters easily. To cancel the ALPHA setting, press ;. 2. Enter the title of the file (up to seven characters). • If you change your mind and no longer want to save the equation, press j. SAVE:RING_ “RING” is entered as the file name. Press e to save the equation. 3. • The display returns to the display before pressing f. Note: • When saving an equation, local variables (including their values) used in the equation are saved at the same time. 58 Chapter 3: Scientific Calculations Loading and deleting an equation The procedures to retrieve (load) and delete an equation from memory are the same, except that you have to confirm that you wish to delete the equation. Retrieve or delete an equation as follows. 1. Press f and then 0 or 2 to retrieve (load) or delete. 2. Use d u to select the name of the file you wish to retrieve (or delete),and press e. DEL ¬º⁄RING º¤AREA-3 º‹CIRCUIT DEL has been selected. • The display asks for confirmation if you are deleting an equation. Press y to proceed with deletion or e to cancel the operation. TITLE:RING DELETE¬[DEL] QUIT¬[ENTER] Note: • If the equation being retrieved contains local variables, the local variable names and their values will be retrieved along with the equation. • Any other equation on the display and local variables before the equation was retrieved are cleared. 59 60 Chapter 4: Statistical Calculations The STAT mode is used to perform statistical calculations. Press b 1 to select the statistics mode. The seven statistical calculations listed below can be performed. After selecting the statistics mode, select the desired sub-mode by pressing the number key that corresponds to your choice. To change statistical sub-mode, reselect statistics mode (press b 1), then select the required sub-mode. 0 (SD) : Single-variable statistics 1 (LINE) : Linear regression calculation 2 (QUAD) : Quadratic regression calculation 3 (EXP) : Exponential regression calculation 4 (LOG) : Logarithmic regression calculation 5 (POWER) : Power regression calculation 6 (INV) : Inverse regression calculation 61 Chapter 4: Statistical Calculations The following statistics can be obtained for each statistical calculation (refer to the table below): Variables Q W Contents Key operations n Number of samples I00 ¯x Mean of samples ( x data) I01 sx Sample standard deviation (x data) I02 σx Population standard deviation ( x data) I03 Σx Sum of samples (x data) I04 Σ x2 Sum of squares of samples (x data) I05 ¯y Mean of samples ( y data) I06 sy Sample standard deviation (y data) I07 σy Population standard deviation ( y data) I08 Σy Sum of samples ( y data) I09 Σy 2 Sum of squares of samples ( y data) I0A Σ xy Sum of products of samples (x, y ) I0B a Coefficient of regression equation I20 b Coefficient of regression equation I21 c Coefficient of quadratic regression equation I22 r Correlation coefficient I23 • Use I key to perform a STAT variable calculation. Single-variable statistical calculation Statistics of 1 and value of the normal probability function Linear regression calculation Statistics of 1 and 2 (except coefficients c) and, in addition, estimate of y for a given x (estimate y´) and estimate of x for a given y (estimate x´) Exponential regression, logarithmic regression, power regression, and inverse regression calculation Statistics of 1 and 2 (except coefficients c). In addition, estimate of y for a given x (estimate y´) and estimate of x for a given y (estimate x´). (Since the calculator converts each formula into a linear regression formula before actual calculation takes place, it obtains all statistics, except coefficients a and b, from converted data rather than entered data.) 62 Chapter 4: Statistical Calculations Quadratic regression calculation Statistics of 1 and 2 and coefficients a, b, c in the quadratic regression formula (y = a + bx + cx2). (For quadratic regression calculations, no correlation coefficient (r) can be obtained.) Data Entry and Correction All data entered is kept in memory until STAT memory clear (@ P 2 y) is operated or a new STAT sub-mode is selected. Before entering new data, clear the memory contents. Data entry Single-variable data Data _ Data , frequency _ (To enter multiples of the same data) Two-variable data Data x , Data y _ Data x , Data y , frequency _ (To enter multiples of the same data x and y.) • Up to 100 data items can be entered. With single-variable data, a data item without frequency assignment is counted as one data item, while an item assigned with frequency is stored as a set of two data items. With twovariable data, a set of data items without a frequency assignment is counted as two data items, while a set of items assigned with frequency is stored as a set of three data items. Data correction Correction prior to pressing _ immediately after a data entry: Delete incorrect data with j, then enter the correct data. 63 Chapter 4: Statistical Calculations Correction after pressing _: Use u d to display the data set previously entered. Press d to display the data set in ascending (oldest first) order. To reverse the display order to descending (latest first), press the u key. Each data set is displayed with ‘X=’, ‘Y=’, or ‘N: ’ (N is the sequential number of the data set). Data set number X=z › 75. 3. Data x Frequency Data set number X=z Y= › 4. 3. 3. Data x Data y Frequency Display and move the cursor to the data item to be modified by using u d, input the correct value, then press _ or e. • To delete a data set, display and move the cursor to an item of the data set to delete by using u d, then press @ #. The data set will be deleted. • To add a new data set, press j to exit the display of previously entered data and input the values, then press _. Example DATA 30 40 40 50 DATA 30 45 45 45 60 64 Key operations b10 Result Stat 0 [SD] 0. 30 _ 40 , 2 _ DATA SET= DATA SET= 1. 2. 50 _ DATA SET= 3. ddd 45 _ 3_ X= ¤ 45. 3. d 60 _ X= 60. Chapter 4: Statistical Calculations Statistical Calculation Formulas Type Linear Exponential Logarithmic Power Inverse Quadratic Regression formula y = a + bx y = a • ebx y = a + b • ln x y = a • xb 1 y=a+b— x y = a + bx + cx2 In the statistical calculation formulas, an error will occur if: • The absolute value of an intermediate result or calculation result is equal to or greater than 1 × 10100. • The denominator is zero. • An attempt is made to take the square root of a negative number. • No solution exists for a quadratic regression calculation. x = Σnx σx = Σ x = x1 + x2 + ··· + xn y= Σy n Σ x2 – nx2 n sx = Σ x2 – nx2 n–1 Σ x2 = x12 + x22 + ··· + xn2 σy = Σ xy = x1y1 + x2y2 + ··· + xnyn Σ y2 – ny2 n Σ y = y1 + y2 + ··· + yn sy = Σ y2 – ny2 n–1 Σ y2 = y12 + y22 + ··· + yn2 65 Chapter 4: Statistical Calculations Normal Probability Calculations • P(t), Q(t), and R(t) will always take positive values, even when t<0, because these functions follow the same principle used when solving for an area. • Values for P(t), Q(t), and R(t) are given to six decimal places. – t = xσ–x x 66 Standardization conversion formula Chapter 4: Statistical Calculations Statistical Calculations Examples Example Key operations Result @P2y DATA 95 80 80 75 75 75 50 – x= σx = n= Σx = Σx 2 = sx = sx2 = (95–– x) ×10+50= sx b10 Stat 0 [SD] 0. 95 _ 80 _ _ 75 , 3 _ DATA DATA DATA DATA SET= SET= SET= SET= 1. 2. 3. 4. 50 _ DATA SET= 5. I01e I03e I00e I04e I05e I02e Ae ˛= 75.71428571 σ≈= 12.37179148 ( 95 - I 0 1 ) z I 0 2 k 10 + 50 e x = 60 → P(t) ? I 1 1 60 I 1 0 )e t = –0.5 →R(t) ? I 1 3 S 0.5 ) e n= 7. Í≈= 530. Í≈Œ= 41200. sx= 13.3630621 178.5714286 64.43210706 0.102012 0.691463 67 Chapter 4: Statistical Calculations Example Key operations Result @P2y DATA x y 2 2 12 21 21 21 15 5 5 24 40 40 40 25 a= b= r= sx = sy = x=3 → y'=? y=46 → x' =? b11 Stat 1 [LINE] 0. 2,5_ _ 12 , 24 _ 21 , 40 , 3 _ DATA DATA DATA DATA SET= SET= SET= SET= 1. 2. 3. 4. 15 , 25 _ DATA SET= 5. I20e I21e I23e I02e I07e a= 1.050261097 b= 1.826044386 r = 0.995176343 sx =8.541216597 sy =15.67223812 3I25 46 I 2 4 6.528394256 24.61590706 @P2y b12 Stat 2 [QUAD] 0. 12 , 41 _ 8 , 13 _ 5,2_ 23 , 200 _ 15 , 71 _ DATA DATA DATA DATA DATA I20e I21e I22e a= 5.357506761 b=-3.120289663 c= 0.503334057 x=10 → y' =? 10 I 2 5 y = 24.4880159 y=22 → x' =? 22 I 2 4 ≈¡: 9.63201409 ≈™:-3.432772026 DATA x y 12 41 8 13 5 2 23 200 15 71 a= b= c= 68 SET= SET= SET= SET= SET= 1. 2. 3. 4. 5. Chapter 5 Equation Solvers Simultaneous Linear Equations Simultaneous linear equations with two unknowns (2-VLE) or with three unknowns (3-VLE) may be solved using this function. 1 2-VLE: b 3 0 a1x + b1y = c1 a2x + b2y = c2 D = a1 b1 a2 b2 D = a1 b1 c1 a2 b2 c2 a3 b3 c3 2 3-VLE: b 3 1 a1x + b1y + c1z = d1 a2x + b2y + c2z = d2 a3x + b3y + c3z = d3 • If the determinant D = 0, an error occurs. • If the absolute value of an intermediate result or calculation result is equal to or greater than 1 × 10100, an error occurs. • The results obtained by this function may include a margin of error. Example 1 2x+3y = 4 5x+6y = 7 Ò x=? y=? det(D) = ? 1. 2. Press b 3 0 to select 2VLE of the EQN mode. a⁄z b⁄ c⁄ 0. 0. 0. Enter the value of each coefficient (a1, etc.) 2e3e4e 5e6e7 • Coefficients can be entered using ordinary arithmetic operations. • To clear the entered coefficients, press j. • Press d or u to move line by line. Press @ d or @ u to jump to the last or top line. 69 Chapter 5: Equation Solvers 3. After inputting the last coefficient, press e to solve the 2-VLE. • After solving, press e or j to return to the coefficient entering display. You can use @ h to solve the 2VLE, regardless of the cursor position. x= y= D= –1. 2. –3. a⁄z b⁄ c⁄ 0. 0. 0. Example 2 x+y-z = 9 6x+6y-z = 17 14x-7y+2z = 42 x=? Ò y=? z=? det(D) = ? 1. 2. Press b 3 1 to select 3VLE of the EQN mode. Enter the value of each coefficient (a1, etc.) 1e1eS1e9e 6 e 6 e S 1 e 17 e 14 e S 7 e 2 e 42 • Coefficients can be entered using ordinary arithmetic operations. • To clear the entered coefficients, press j. • Press d or u to move line by line. Press @ d or @ u to jump to the last or top line. 3. After inputting the last coefficient, press e to solve the 3-VLE. • Press d to display the det(D). • After solving, press e or j to x= 3.238095238 return to the coefficient entering display. y=–1.638095238 You can use @ h to solve the 3Z= –7.4 VLE, regardless of the cursor position. D= 70 105. Chapter 5: Equation Solvers Quadratic and Cubic Equation Solvers Quadratic (ax2 + bx + c = 0) or cubic (ax3 + bx2 + cx + d = 0) equations may be solved using these functions. 1 Quadratic equation solver (QUAD): b 3 2 2 Cubic equation solver (CUBIC): b 3 3 • If there are more than 2 results, the next solution can be displayed. • The results obtained by this function may include a margin of error. Example 1 3x2 + 4x – 95 = 0 → x = ? 1. 2. Press b 3 2 to select QUAD of the EQN mode. a=z b= 0. 0. Enter the value of each coefficient (a, c= 0. etc.) 3 e 4 e S 95 • Coefficients can be entered using ordinary arithmetic operations. • To clear the entered coefficients, press j. • Press d or u to move line by line. 3 After inputting the last coefficient, press e to solve the quadratic X⁄ 5. equation. X¤–6.333333333 • After solving, press e or j to return to the coefficient entering display. You can use @ h to solve the quadratic equation, regardless of the cursor position. 71 Chapter 5: Equation Solvers Example 2 5x3 + 4x2 +3x + 7 = 0 → x = ? 1. Press b 3 3 to select CUBIC of the EQN mode. a=z b= c= 0. 0. 0. 2. Enter the value of each coefficient (a, etc.) 5e4e3e7 • Coefficients can be entered using ordinary arithmetic operations. • To clear the entered coefficients, press j. • Press d or u to move line by line. Press @ d or @ u to jump to the last or top line. 3. After inputting the last coefficient, press e to solve the cubic equation. • After solving, press e or j to return to the coefficient entering display. You can use @ h to solve the cubic equation, regardless of the cursor position. 72 X⁄–1.233600307 X¤ 0.216800153 +1.043018296i - Chapter 6 Complex Number Calculations The CPLX mode is used to carry out addition, subtraction, multiplication, and division of complex numbers. Press b 4 to select the CPLX mode. Results of complex number calculations are expressed in two modes: 1 @ E: Rectangular coordinates mode (xy appears.) 2 @ u: Polar coordinates mode (rθ appears.) Complex Number Entry 1 Rectangular coordinates are entered as follows: x-coordinate + y-coordinate Q or x-coordinate + Q y-coordinate 2 Polar coordinates are entered as follows: r Rθ r: absolute value θ:argument • On selecting another mode, the imaginary part of any complex number stored in the M memory will be cleared. • A complex number expressed in rectangular coordinates with the y-value equal to zero, or expressed in polar coordinates with the angle equal to zero, is treated as a real number. • Press I 0 to return the complex conjugate of the specified complex number. 73 Chapter 6: Complex Number Calculations Example Key operations b4 (12–6i) + (7+15i) – (11+4i) = 6×(7–9i) × (–5+8i) = 16×(sin30°+ icos30°)÷(sin60°+ icos60°)= ( 12 - 6 Q ) + ( 7 + 15 Q ) ( 11 + 4 Q ) e 6k( 7-9Q) k(S5+8Q )e 16 k ( v 30 + Q $ 30 ) z ( v 60 + Q $ 60 ) e @ u 8 R 70 + 12 R 25 e Result COMPLEX MODE 0. 8. +5.i 222. +606.i 13.85640646 +8.i 18.5408873 ∠ 42.76427608 r1 = 8, θ1 = 70° r2 = 12, θ2 = 25° ↓ r = ?, θ = ?° (1 + i) ↓ r = ?, θ = ?° @E1+Qe (2 – 3i)2 = @E(2-3Q )Ae @u 1 = 1+i (1+Q)@ Ze conj(5+2i) = I0(5+2Q )e 74 1. +1.i 1.414213562 ∠ 45. –5. –12.i 0.5 –0.5i 5. –2.i Chapter 7 Programming PROG mode A program enables you to automate a series of calculations, including those simple and complex. Programs are created either in the NORMAL program mode or in the NBASE program mode. Entering the PROG mode 1. Press b 2 to select the PROG (PROGRAM) mode. 2. Press 0 to RUN a program, press 1 to create a NEW program, press 2 to EDIT a program, and press 3 to DELETE a program. PROGRAM MODE ƒRUN ⁄NEW ¤EDIT ‹DEL Selecting the NORMAL program mode or the NBASE program mode Before creating a new program (b 2 1), select either the NORMAL program mode or the NBASE program mode. In the NORMAL program mode, you can perform simple mathematical calculations and statistical operations. In the NBASE program mode, you can perform logical operations and calculations using N-base numbers. Programming concept It is not within the scope of this manual to describe how to write programs for the calculator in detail. Previous programming experience is required to read this section. The programming language for this calculator is similar to those in general use today. All conventional computer and calculator programs use fundamental elements such as input, flow control, loops, calculation, and output. The programming language in your calculator includes commands that allow you to incorporate all of these fundamental elements into your programs. For the command list, refer to the ‘Programming Commands.’ (See page 79.) Note: • Commands must be entered using the COMMAND menu (i). DO NOT type commands manually using the ; key. 75 Chapter 7: Programming Keys and display In the PROG mode, to make programs as simple as possible, some keys and the display may work in a different manner to other modes. The differences are described below. • Press i (the f key) to directly access the command menu for programming. The Filing Equation function does not work in PROG mode. • While entering a program name, keys are locked in ALPHA mode (ALOCK) automatically. • In a program, a single line can hold up to 159 letters, where all commands are counted as a single letter. As you type in a line, the text will scroll to the left. Lines do not wrap in the PROG mode. Creating a NEW Program After you name the program, the calculator automatically stores the whole program under this name as you create it. You do not have to save the program manually. Creating a NEW program Press b 2 to enter the PROG mode and then press 1 to create a NEW program. 1. • The display prompts you to select the NORMAL program mode or the NBASE program mode. For this example, press 0 to select the NORMAL program mode. 2. MODE ƒNORMAL ⁄NBASE TITLE? :NORMAL • The display prompts you to enter a program name. 3. Type the name of the program (i.e., SLOPE). SLOPE_ :NORMAL • A program name can have up to 7 letters. • The calculator automatically switches to the alphabet-lock mode. You do not have to press the ; key each time before entering an alphabetic character. After completion, press e. 4. • You are now ready to write a program. SLOPE :NORMAL PROGRAM? • Each program line is saved after you press u, d or e. • You can use the calculator’s regular functions as commands. You can also use the additional programming commands in the i menu. 76 Chapter 7: Programming Use of variables Global and local variables are treated differently in the PROG mode. • The letters A – Z and θ, used on their own, represent global variables. Global variables correspond to the memories of the calculator (e.g., ‘C’ in a program means memory C of the calculator). Global variables allow your programs to use values stored in memories, or to pass variables from one program to another. Global variables also allow you to store results from programs and use them in any mode. • You can also name and use up to nine local variables (@ v). Local variables retain values only in an individual program. If a line in your program contains an equation such as Y = M1X + 5, it sets the global variable Y equal to (M1 × X) + 5. On encountering this equation while running the program, if the value of the local variable M1 has not been defined earlier in the program, the calculator prompts you with the display ‘M1=?’ to enter a value for M1. The global variable X will already be set to the value last stored in that memory. SLOPE :NORMAL Y=M¡X+5 _ SLOPE :NORMAL M¡=? With just a little practice you will soon become proficient at typing programs into your calculator. Example Create a simple program that requests input of the base length (B1) and height (H1) of a triangle and then calculates the area (A). After creating, RUN the program to determine the area of a triangle with a base of 4 units and a height of 3 units. 1. Preparing to create a NEW program Procedure Key operations Select the NORMAL program mode. b2 1 0 Type the program name. AREA Enter the program name. e Enter the PROG mode. Select NEW. Display AREA :NORMAL PROGRAM? 77 Chapter 7: Programming 2. Entering the program Program code Key operations Print“B≥=BASE i 1 @ v B1 e e @ a = BASE ; e Print“H≥=HEIGHT i 1 @ v d H1 e e @ a = HEIGHT ; e A=1ı2B≥H≥ ;A;=1k2@v e@vdee Print“AREA i 1 @ a AREA ; e Print A i0;Ae • To enter more than one alphabetic character, press @ a to apply the alphabet-lock mode. Press ; to escape from this mode. 3. Running the program Procedure Return to the initial display for the PROG mode. Key operations Display j Select and RUN the program. 0 (Select the program.) RUN ¬º⁄AREA e Enter 4 for B1 4e Enter 3 for H1 3e AREA A= 6. • If the value of a local variable you defined using @ v is unknown, the program automatically prompts you to input a value. • To quit running the program, press j. To run the program again, press e. • When a program is running, text displayed by the program (using the Print” command) will wrap to the next line if the text length exceeds the display width. • You can only enter one command per line except for special cases such as the ‘If…Goto’ structure. • For more programming examples, see Chapter 8: Application Examples. 78 Chapter 7: Programming Programming Commands In this section, all commands that are available in the PROG mode are described, excluding keyboard commands and I menu commands. Input and display commands 1. While creating a NEW or EDIT program, press i to access the COMMAND menu. <COMMAND-1> ƒPrint ⁄Print" ¤Input ‹Wait • The first page of the COMMAND menu is displayed. • Press d or u to scroll page by page. • You may directly enter a command by pressing the corresponding alphanumeric key without first having to display the relevant COMMAND menu page. Key Command operations i0 Print <variable> Description Examples Displays the value of the specified variable. The display format is determined by the SET UP menu. Print A Print B≥ Displays the text entered after the quotation mark. If the text exceeds three lines, only the last three lines will be displayed. Print” SHARP Input i2 <variable> Temporarily stops the program and prompts you to enter a value for the variable with the display ‘<variable>=?’. Input A Input B≥ i3 Pauses the program for the specified number of seconds. The maximum wait time is 255 seconds. If no wait time is specified, the program pauses until you press any of the keys. The BUSY indicator stays on while the program is waiting. Wait 5 Wait FF (hexadecimal mode) Print” <text> Wait <number> i1 Wait 1010 (binary mode) 79 Chapter 7: Programming Command 80 Key operations Description Examples Rem <text> i4 Indicates the line is a remark and not a command, thus allowing you to insert comments in the program. Any line beginning with Rem is ignored when running a program. Excessive use of this command will use up a considerable amount of memory. Rem TIME TABLE End i5 Terminates the program. If the program finishes at the last command, an End command is not required. If there is no End command in the program, the last calculated answer will be displayed when the program finishes. You can use more than one End command in the same program to terminate after different branches, subroutines, etc. have been executed. End Chapter 7: Programming Flow control Key Command operations Description Examples i6 Label <label name> Indicates a destination point for the flow statements Goto and Gosub. Up to seven letters can be used for the label name. Each label name must be unique. You cannot use the same label name more than once in a program. Up to 20 different labels can be used in each program. Label LOOP1 Label LOOP2 Clear the text displayed on the screen. Clrt i8 If <condition> i9 Goto <label name> The If clause must be followed by a conditional statement and then a Goto command. Goto is the only command allowed to be used after the If clause. You can enter ; s before the Goto command to make the line easier to read. If B≥=1 Goto LOOP1 i9 Goto <label name> Causes the program to jump to the stated Label (specified by a Label command). A Goto statement must have a corresponding Label statement line that indicates where to go. Goto LOOP2 iA Gosub <label name> Runs the subroutine beginning at the stated Label (specified by a Label command). A Gosub statement must have a corresponding subroutine that starts after the Label statement and ends with a Return command. Subroutines can be nested up to ten levels deep. Gosub PART1 iB Defines the end of a subroutine. Operation returns to the command following the corresponding Gosub statement. Return Clrt Return i7 81 Chapter 7: Programming Equalities and inequalities These expressions are used to form the conditional statement in the If clause. They are the basis for looping and other flow control operation in programs. The ‘=’ (equals) sign is also used as a function to form a substitution command for variables. You can also enter ‘=’ by simply pressing ; =. Symbols Key operations Examples iC Equals. This function is also If B=0 Goto ZERO used to form a substitution A=A+1 command that assigns a new value to a variable, including incrementing or decrementing. < iD Less than If B<0 Goto NGTV <= iE Less than or equal to. If B≥<=0 Goto CALC >= iF Greater than or equal to. If B>=0 Goto RECALC > iG Greater than If B≥>0 Goto PSTV ≠ iH Not equal to. If A≠B Goto DIF = 82 Description Chapter 7: Programming Statistical Commands In the PROG mode, statistical commands are only available when the NORMAL program mode is selected. If the NBASE program mode is selected, the statistical command menu cannot be called. • When you use the STATx or STATxy commands, the calculator erases all data previously stored in the STAT function. Command Key operations STATx iI Selects single-variable statistics mode (SD). STATx STATxy iJ Selects linear regression calculation mode (LINE). STATxy Data <x> iK Enters new statistical data. The data format must be consistent with the statistics mode selected (singlevariable or linear regression). A statistical data set entered in the PROG mode cannot be accessed later for use with STAT functions. Data <x, frequency> Data <x, y> Data <x, y, frequency> Description Examples Data 5 Data 25,2 Data 72,175 Data 9,96,3 83 Chapter 7: Programming Editing a Program 1. Press b 2 to enter the PROG mode and then press 2 to select the EDIT mode. 2. Select the program you wish to edit and press e. • If you want to add text into your program, press @ O. • If you want to add lines into your program, press @ O (the shape of the cursor will become a triangle) and then move the cursor to the beginning of the line and press e to add a new line there. • Remember that you can enter only one command per line except in the special case of the ‘If…Goto’ command. Do not try to enter two or more commands on a single line. • The line you modify is saved after you press u, d or e. If you do not wish to change the line, press j twice. (The line will disappear at this point, however, the contents of the line are not deleted.) • To clear an entire line of a program, press j then u, d or e. To delete a blank line, move the cursor to the blank line and press y. • Any blank lines will be ignored when running. • y deletes the character you have just entered (the character at the cursor position). • You can change the name of a program by overwriting the existing name. Press u to move the cursor to the title line and type the new name and press e. 3. 84 Press j to exit the EDIT mode. Chapter 7: Programming Error Messages The calculator displays an error message if a program encounters a problem. The error message indicates the nature of the problem while the calculator can display the line where the problem has occurred. After entering a program, it is often necessary to debug it. To make this task easier, the calculator displays an error message if it encounters a problem while running your program. For example, if you have more than one label with the same name in your program, you will see the message on the right. - ERROR 04 LBL DUPLICATE To display the faulty line in the EDIT mode, press r or l. To return to the program menu, press j. You can press j to stop your program at any time while it is running. This will be necessary if your program enters an endless loop. BREAK! After ‘BREAK!’ is temporarily displayed, the initial PROG mode display will reappear. For a list of error messages, refer to the Appendix. (See page 120.) 85 Chapter 7: Programming Deleting Programs You can create as many programs as you want within the limitations of the calculator’s memory. To free up space for new programs, you must delete old ones. Press b 2 to enter the PROG mode. 1. Press 3. 2. • The delete window appears. All the stored programs are listed. 3. Move the cursor to the program you wish to delete and press e. • The calculator asks you if you are sure you want to delete the program. • Press y to delete the program or e to cancel this operation. 86 PROGRAM MODE ƒRUN ⁄NEW ¤EDIT ‹DEL DEL ¬º⁄AREA º¤TEMP º‹STAT TITLE:AREA DELETE¬[DEL] QUIT¬[ENTER] Chapter 8 Application Examples Programming Examples The following examples demonstrate the basic use of programming commands including print, input and flow controls. Use the examples for your programming reference. Some like it hot (Celsius-Fahrenheit conversion) This is a program to convert temperatures from Celsius to Fahrenheit and vice versa. 1. Press b 2 1 0 to open a window for creating a NEW program. 2. Type TEMP for the program title then press e. • A NEW program called ‘TEMP’ will be created. 3. Enter the program as follows. TEMP :NORMAL PROGRAM? • See ‘*’ below for further explanation. Program code Key operations Label START i 6 @ a START ; e Print”(1) C TO F i 1 ( 1 ) @ a s C s TO s F ; e Print”(2) F TO C i 1 ( 2 ) @ a s F s TO s C ; e Input T i 2 ; T e * Here, the program prompts you to choose which type of conversion you wish to perform. Press 1 for “C TO F” and 2 for “F TO C”. 87 Chapter 8: Application Examples Program code Key operations If T=1 Goto CTOF i 8 ; T ; = 1 ; s i 9 @ a CTOF ; e If T=2 Goto FTOC i 8 ; T ; = 2 ; s i 9 @ a FTOC ; e Goto START i 9 @ a START ; e Label CTOF i 6 @ a CTOF ; e F=(9©5)C≠+32 ; F ; = ( 9 z 5 ) @ v C0 e e + 32 e * The program automatically prompts you to enter a value for the local variable C0. Print F i 0 ; F e End i 5 e Label FTOC i 6 @ a FTOC ; e C=(5©9)˚(F≠-32) ; C ; = ( 5 z 9 ) k ( @ v d F0 e e - 32 ) e * The program automatically prompts you to enter a value for the local variable F0. Print C i 0 ; C e End i 5 e Running the program 4. Press j to return to the PROG mode menu. 5. Press 0, select the program ‘TEMP’ and press e. PROGRAM MODE ƒRUN ⁄NEW ¤EDIT ‹DEL • The program prompts you to choose which conversion you wish to perform. Then it asks you to enter the temperature value. 88 Chapter 8: Application Examples The Heron Formula Obtaining the area S of triangle with side lengths of A, B and C using the Heron Formula which is true for any plane triangle. 1. Press b 2 1 0 to open a window for creating a NEW program. 2. Type HERON for the program title then press e. B A S C S = √ T (T – A) (T – B) (T – C) A+B+C T = ————— 2 • A NEW program called ‘HERON’ will be created. 3. Enter the program as follows. Program code Key operations Label START i 6 @ a START ; e Print”SIDE LENGTHS i 1 @ a SIDE s LENGTHS ; e Input A i 2 ; A e Input B i 2 ; B e Input C i 2 ; C e If (A+B)<=C Goto ERROR i 8 ( ; A + ; B ) i E ; C ; s i 9 @ a ERROR ; e If (B+C)<=A Goto ERROR i 8 ( ; B + ; C ) i E ; A ; s i 9 @ a ERROR ; e If (C+A)<=B Goto ERROR i 8 ( ; C + ; A ) i E ; B ; s i 9 @ a ERROR ; e T=(A+B+C)©2 ; T ; = ( ; A + ; B + ; C ) z 2 e 89 Chapter 8: Application Examples Program code Key operation S=‰(T(T-A)(T-B)(T-C)) ; ; ) ( e S ; = T ( ; ( ; T ; T - @ * ( T - ; A - ; B ) ; C ) ) Print S i 0 ; S e End i 5 e Label ERROR i 6 @ a ERROR ; e Print”NO TRIANGLE i 1 @ a NO s TRIANGLE ; e Wait 1 i 3 1 e Print”REENTER i 1 @ a REENTER ; e Goto START i 9 @ a START ; e Example Obtain the area of the triangle with the side lengths of 20 cm (A), 35 cm (B) and 40 cm (C). 4. Press j to return to the PROG mode menu. Press 0, select the program ‘HERON’ and press e. 5. HERON :NORMAL SIDE LENGTHS A=? • If the values you enter do not satisfy the conditions to make a triangle (e.g. A + B > C where A, B, C are the side lengths), the program prompts you to reenter the values from the beginning. If you wish to stop the program, press j. 6. Enter 20 for A, 35 for B and 40 for C. Result The area of the triangle is approximately 350 cm2. 90 40 S= 349.944192 Chapter 8: Application Examples 2B or not 2B (N-base conversion) The conversion functions and logical operations can be used in the NBASE program mode. The following is a simple program that converts a decimal number to binary, pental, octal and hexadecimal formats. 1. 2. Press b 2 1 1 to open a window for creating a NEW program in the NBASE program mode. NBASE :NBASE PROGRAM? Type NBASE for the title then press e. • A NEW program called ‘NBASE’ will be created. 3. Enter the program as follows. Program code Key operations Print”ENTER A i 1 @ a ENTER s A ; e Print”DECIMAL NUMBER i 1 @ a DECIMAL s NUMBER ; e Input Y i 2 ; Y e Y¬BIN ; Y @ z e Print”BINARY i 1 @ a BINARY ; e Print Y i 0 ; Y e Wait i 3 e Y¬PEN ; Y @ r e Print”PENTAL i 1 @ a PENTAL ; e Print Y i 0 ; Y e Wait i 3 e 91 Chapter 8: Application Examples Program code Key operations Y¬OCT ; Y @ g e Print”OCTAL i 1 @ a OCTAL ; e Print Y i 0 ; Y e Wait i 3 e Y¬HEX ; Y @ h e Print”HEXADECIMAL i 1 @ a HEXADECIMAL ; e Print Y i 0 ; Y e Running the program 4. Press j to return to the PROG mode menu. 5. Press 0, select the program ‘NBASE’ and press e. • The program prompts you to enter a decimal number and then displays it in binary format. • Press any key to display the number in pental format, then press any key to see it in octal format, and again press any key to see it in hexadecimal format. • Be careful when using the Wait command in NBASE program mode. Numbers followed by Wait are processed according to the current number base, binary, pental, octal, decimal or hexadecimal. To specify the wait time in decimal format, define a variable (e.g., T = 5) for the wait time beforehand and use it in the Wait command (i.e., Wait T). 92 Chapter 8: Application Examples T test The T-test value is obtained by comparing the mean values of sample data and expected average from sample data. Using the t- distribution table, the reliability of a mean value can be evaluated. –x – m t = ——— sx2 —— n m = expected mean value estimated by sample data n = the number of samples –x = actual mean value of the samples sx = standard deviation of the samples Example A’s SHOP sells cookies by package on which it is stated contents are 100 g. Buy 6 sample packages and check if the statement is true. • Setting an expected mean value as 100 (m = 100 g), a t-test value is obtained. If it is larger than the expected t-value obtained from a tdistribution table (at 5% of risk rate), the estimation is wrong. (In this case, A’s SHOP does not sell honestly.) Sample grams 1. 2. 1 2 3 4 5 6 102 95 107 93 110 98 Press b 2 1 0 to open a window for creating a NEW program. Type TTEST for the title then press e. • A NEW program called ‘TTEST’ will be created. 3. Enter the program as follows. 93 Chapter 8: Application Examples Program code Key operations STATx iIe Data 102 i K 102 e Data 95 i K 95 e Data 107 i K 107 e Data 93 i K 93 e Data 110 i K 110 e Data 98 i K 98 e Print”MEAN i 1 @ a MEAN ; e Input M i2; M e T=(˛-M)©‰(sxŒ©˜) ; 1 * I Print T i0; T e End i5 e T ;=(I5 -; M )z@ (I52Az 50)e Running the program 4. Press j to return to the PROG mode menu. 5. Press 0, select the program ‘TTEST’ and press e. 6. Enter the expected mean value ‘100’ and press e. T= 0.303058133 Result The t-test value of 0.303 is smaller than the 2.571, expected mean value obtained from a t-test distribution table (at 5% of risk rate), showing that they sell honestly. 94 Chapter 8: Application Examples A circle that passes through 3 points When three different points, P (X1, Y1), Q (X2, Y2), S (X3, Y3) are given, obtain the center coordinates O (X, Y) and the radius R of the circle that passes through these points. To satisfy the above conditions, the distances between P, Q, S and O should be equal. as they are the radius of the same circle. Therefore, Q (X2, Y2) R P (X1, Y1) Y1–Y R X1–X PO = QO = SO = R O (X, Y) R Using the Pythagorean theorem, PO2 = (X1 – X)2 + (Y1 – Y)2 = R2 QO2 = (X2 – X)2 + (Y2 – Y)2 = R2 SO2 = (X3 – X)2 + (Y3 – Y)2 = R2 then S (X3, Y3) X= (X12+Y12-X22-Y22)(Y2–Y3) – (X22+Y22-X32-Y32)(Y1–Y2) ------ 1 2{(X1–X2)(Y2–Y3) – (X2–X3)(Y1–Y2)} Y= (X12+Y12-X22-Y22)(X2–X3) – (X22+Y22-X32-Y32)(X1–X2) ------ 2 2{(Y1–Y2)(X2–X3) – (Y2–Y3)(X1–X2)} R = (X – X1)2 + (Y – Y1)2 ------ 3 To enhance both readability and writability of the program, intermediate variables G, H, I, J, K and M are used. The above equations reduce to X= GM – HK 2 (IM – JK) Y= GJ – HI 2 (KJ – MI) 1. Press b 2 1 0 to open a window for creating a NEW program. 2. Type CIRCLE for the title then press e. • A NEW program called ‘CIRCLE’ will be created. 3. Enter the program as follows. Program code Key operations Print”ENTER COORDS i 1 @ a ENTER s COORDS ; e G=X≥Œ+Y≥Œ-X√Œ-Y√Œ ; e e e d * Calculate intermediate values. G ; = @ v X1 e A + @ v d Y1 e A - @ v d d X2 e A - @ v d d Y2 e e A e 95 Chapter 8: Application Examples Program code Key operations H=X√Œ+Y√Œ-X…Œ-Y…Œ ; H; = @ v 2 A + @ v 3 A - @ v d d d d X3 e e A - @ v d d d d d Y3 e e A e I=X≥-X√ ; I ; = @ v 0 @ v 2 e J=X√-X… ; J ; = @ v 2 @ v 4 e K=Y≥-Y√ ; K ; = @ v 1 @ v 3 e M=Y√-Y… ; M ; = @ v 3 @ v 5 e X=(GM-HK)©2(IM-JK) ; X ; = ( ; G; M ; H ; K) z 2( ; I ; M - ; J ; K) e * Perform equation 1. Print X i 0 ; X e Wait i 3 e Y=(GJ-HI)©2(KJ-MI) ; Y ; = ( ; G; J ; H ; I) z 2( ; K ; J - ; M ; I) e * Perform equation 2. Print Y i 0 ; Y e Wait i 3 e R=‰((X-X≥)Œ+(Y-Y≥)Œ) ;R;=@* ((; X -@ v0)A+( ; Y-@v 1)A)e * Perform equation 3. Print R i 0 ; R e Example Obtain the center coordinates (X, Y) and radius R of the circle that passes through points P(1, 9), Q (7, 1) and S (0, 2). 4. Press j to return to the PROG mode menu. 5. Press 0, select the program ‘CIRCLE’ and press e. 6. Enter the coordinates (X 1 to X3, Y1 to Y3) for the three points. Result The center is (4, 5) and radius is 5. 96 Chapter 8: Application Examples Radioactive decay Carbon-14 (14C) is a naturally occurring radioactive isotope of carbon used in the carbon dating process. Because carbon-14 decays at a steady rate, it is possible to determine the age of a once living specimen by measuring the residual amount of 14C it contains. The mass of 14C contained in a sample changes according to the equation M1 –ln ( ––– ) M0 –kt M = M0 e or t = ––––––––– k where M1 = Mass of 14C at time t M0 = Original mass of 14C k = Radioactive decay constant (for 14C, k = 1.2118 × 10–4 year–1) t = Elapsed time in years Example This program asks for a original mass and current mass of 14C and tells you how old the specimen is. It then finds the half-life of 14C. 1. Press b 2 1 0 to open a window for creating a NEW program. 2. Type DECAY for the title then press e. • A NEW program called ‘DECAY’ will be created. 3. DECAY :NORMAL PROGRAM? Enter the program as follows. Program code Key operations Print”ORIGINAL MASS i 1 @ a ORIGINAL s MASS ; e Input M≠ i 2 @ v M0 e e e Print”CURRENT MASS i 1 @ a CURRENT s MASS ; e Input M≥ i 2 @ v d M1 e e e 97 Chapter 8: Application Examples Program code Key operations T=-(ln(M≥©M≠))© ; T ; = S ( i 1.2118œ-4 ( @ v 1 z @ v 0 ) ) z 1.2118 ` S 4 e Print T i 0 ; T e Print”YEARS i 1 @ a YEARS ; e End i 5 e • The half-life of a radioactive isotope is the time required for half of its mass to decay. Running the program 4. Press j to return to the PROG mode menu. 5. Press 0, select the program ‘DECAY’ and press e. Enter 100 for M0 and 50 for M1 . 6. Result The half-life of 14C is 5719.980034 years. 98 DECAY :NORMAL ORIGINAL MASS Mº=? T= 5719.980034 YEARS Chapter 8: Application Examples Delta-Y impedance circuit transformation Transformation of a Y impedance circuit to an equivalent Delta impedance circuit and vice versa. The Delta-Y transformation is defined by the following formula: Z2 R1 R Z1 = — R2 R Z2 = — R3 R Z3 = — R1 Z1 Z3 where R = R1R2 + R2R3 + R3R1 1. 2. Z1 Z2 R1 = ——— Z Z 2 Z3 R2 = ——— Z Z 3 Z1 R3 = ——— Z R2 R3 where Z = Z1 + Z2 + Z3 Press b 2 1 0 to open a window for creating a NEW program. Type DELTAY for the title then press e. • A NEW program called ‘DELTAY’ will be created. 3. Enter the program as follows. Program code Key operations Print”(1)DELTA TO Y i 1 ( 1 ) @ a DELTA s TO s Y ; e Print”(2)Y TO DELTA i 1 ( 2 ) @ a Y s TO s DELTA ; e Input X i 2 ; X e If X=1 Goto DTOY i 8 ; X ; = 1 ; s i 9 @ a DTOY ; e If X=2 Goto YTOD i 8 ; X ; = 2 ; s i 9 @ a YTOD ; e Label DTOY i 6 @ a DTOY ; e 99 Chapter 8: Application Examples Program code Key operations Z=Z≥+Z√+Z… ; e e d R≥=Z≥Z√©Z @ v d d d R1 e e ; = @ v 0 @ v 1 z ; Z e Print R≥ i 0 @ v 3 e Wait i 3 e R√=Z√Z…©Z @ v d d d d R2 e e ; = @ v 1 @ v 2 z ; Z e Print R√ i 0 @ v 4 e Wait i 3 e R…=Z…Z≥©Z @ d v ; Print R… i 0 @ v 5 e End i 5 e Label YTOD i 6 @ a YTOD ; e R=R≥R√+R√R…+R…R≥ ; @ 4 v Z≥=R©R√ @ v 0 ; = ; R z @ v 4 e Print Z≥ i 0 @ v 0 e 100 Z ; = @ v Z1 e + @ v d Z2 e + @ v d Z3 e e e v d d d d R3 e e ; = @ 2 @ v 0 z Z e R ; = @ v 3 v 4 + @ v @ v 5 + @ 5 @ v 3 e Chapter 8: Application Examples Program code Key operations Wait i 3 e Z√=R©R… @ v 1 ; = ; R z @ v 5 e Print Z√ i 0 @ v 1 e Wait i 3 e Z…=R©R≥ @ v 2 ; = ; R z @ v 3 e Print Z… i 0 @ v 2 e End i 5 e Example When the impedances Z1, Z2, Z3 of a delta impedance circuit are 70, 35, 140 respectively, obtain the impedances R1, R2, R3 of a Y circuit. 4. Press j to return to the PROG mode menu. 5. Press 0, select the program ‘DELTAY’ and press e. The direction of transformation will be asked. (1)DELTA TO Y (2)Y TO DELTA X=? 6. Press 1 e to select ‘DELTA TO Y’ transformation. 7. Enter 70 for Z 1, 35 for Z2 and 140 for Z3 . Result The impedances R1, R2, R3 of the targeted Y impedance circuit are 10, 20 and 40, respectively. 101 Chapter 8: Application Examples Obtaining tensions of strings Suppose a bar is hung from the ceiling by two strings such that it balances with angles the strings make from the perpendicular lines A and B. If the weight of the bar is W, obtain the tensions in the strings S and T. S T W —— = —— = ————— sin A sin B sin (A + B) sin B T = W ————— sin (A + B) sin A S = W ————— sin (A + B) where W: weight T, S: tension in strings A, B: angles that strings make from perpendicular lines (DMS) G: gravity Perpendicular line A G S B T B S W W A T Press b 2 1 0 to open a window for creating a NEW program. 1. Type TENSION for the title then press e. 2. • A NEW program called ‘TENSION’ will be created. 3. Enter the program as follows. Program code Key operations Print“ANGLES i 1 @ a ANGLES ; e Input A i 2 ; A e Input B i 2 ; B e Print”WEIGHT i 1 @ a WEIGHT ; e Input W i 2 ; W e C=AΩDEG ; C ; = ; A @ : e D=BΩDEG ; D ; = ; B @ : e 102 Chapter 8: Application Examples Program code Key operations E=sin(C+D) ; E ; = v ( ; C + ; D ) e S=W ˚ sin C©E @ a S = W ; k v ; C z ; E e T=W ˚ sin D©E @ a T = W ; k v ; D z ; E e Print”TENSIONS i 1 @ a TENSIONS ; e Print S i 0 ; S e Wait i 3 e Print T i 0 ; T e End i 5 e Example Calculate the tension in the strings S and T when the weight of the bar is 40 kg, angle A: 30° 15' 20" and angle B: 27° 45' 40". 4. Press j @ J 0 0 to set the angular unit to DEG, then @ J 1 0 3 to set display to fixed mode with the decimal point of 3 . • In this program input angles by degree/minute/second format. They will be automatically converted to decimal degrees. 5. Press b 2 0, select the program ‘TENSION’ and press e. 6. Enter 30 [ 15 [ 20 for angle A and press e. 7. Enter 27 [ 45 [ 40 for angle B and press e. 8. Enter 40 for weight W and press e for S. 9. Press e for T. Results Tension in the strings S and T are 23.761 kg and 21.966 kg, respectively. 23.761 T= 21.966 103 Chapter 8: Application Examples Purchasing with payment in n-month installments If you wish to buy goods with the price of P by n-month installments, this program determines the payment per month. i S = (P – D) ————— 1 – (1 + i)–n where S: payment due every month n : n-month installment P: price of the product D: down payment i: installment payment interest rate (%) Press b 2 1 0 to open a window for creating a NEW program. 1. Type PAYBYMN for the title then press e. 2. • A NEW program called ‘PAYBYMN’ will be created. 3. Enter the program as follows. Program code Key operations Print”PRICE i 1 @ a PRICE ; e Input P i 2 ; P e Print”DOWN PAYMENT i 1 @ a DOWN s PAYMENT ; e Input D i 2 ; D e Print”MONTHS i 1 @ a MONTHS ; e Input N i 2 ; N e Print”RATE i 1 @ a RATE ; e Input I i 2 ; I e I=I©100 ; I ; = ; I z 100 e S=(P-D)˚I©(1-(1+I)^(-N)) ; ; ( 104 S ; = D ) k ( 1 + S ; N ( ; ; ) ; P I z ( 1 I ) m ) e Chapter 8: Application Examples Program code Print S Key operation i 0 ; S e Example If you wish to buy furniture costing $3,000 with $500 as a down payment and pay the remainder in 11 month’s installments with a monthly interest rate of 1%, how much is the monthly payment? 4. Press j to return to the PROG mode menu. 5. Press 0, select the program ‘PAYBYMN’ and press e. 6. Enter 3000 for P, 500 for D, 11 for N and 1 for I. PAYBYMN:NORMAL PRICE P=? Result Your monthly payment is approx. $241. 1 S= 241.1351893 105 Chapter 8: Application Examples Digital dice This program simulates rolling of multiple dice. You can play a dice game without dice or where there is not enough space to roll dice. At the first stage, ask the number of dice to use for play. Secondly, roll dice and display the result and wait until any key is pressed. Press b 2 1 0 to open a window for creating a NEW program. 1. Type DICE for the title then press e. 2. • A NEW program called ‘DICE’ will be created. 3. Enter the program as follows. Program code Key operations Print”NO OF DICE i 1 @ a NO s OF s DICE ; e Input N i 2 ; N e Label PLAY i 6 @ a PLAY ; e M=1 ; M ; = 1 e X=0 ; X ; = 0 e Label ROLL i 6 @ a ROLL ; e X=X+r.dice ; X ; = ; X + @ w 1 e M=M+1 ; M ; = ; M + 1 e If M<=N Goto ROLL i 8 ; M i E ; N ; s i 9 @ a ROLL ; e Print X i 0 ; X e Wait i 3 e Goto PLAY i 9 @ a PLAY ; e Running the program 4. Press j to return to the PROG mode menu. 5. Press 0, select the program ‘DICE’ and press e. 6. Enter the number of dice to play and press e. 7. Press e (or any other key) to continue to play. Press j to quit. 106 Chapter 8: Application Examples How many digits can you remember? The calculator displays randomly created numbers with the number of digits (up to 9) you specified for the number of seconds you entered and asks you to enter the number you remembered. After 10 tries the score is displayed. The larger the number of digits and the shorter the seconds, the higher the score is. 1. 2. Press b 2 1 0 to open a window for creating a NEW program. Type NUMBER for the title then press e. • A NEW program called ‘NUMBER’ will be created. 3. Enter the program as follows. Program code Key operations M=1 ; M ; = 1 e A=0 ; A ; = 0 e Print”HOW MANY DIGITS i 1 @ a HOW s MANY s DIGITS ; e Label NINE i 6 @ a NINE ; e Print”LESS THAN 9 DIGITS i 1 @ a LESS s THAN s ; 9 @ a s DIGITS ; e Input N i 2 ; N e If N>9 Goto NINE i 8 ; N i G 9 ; s i 9 @ a NINE ;e Print”HOW LONG i 1 @ a HOW s LONG ;e Input T i 2 ; T e Label QUESTION i 6 @ a QUESTION ; e Label AGAIN i 6 @ a AGAIN ; e S=ipart(random˚10^3) ; S ; = I 1 ( @ w 0 k @ Y 3 ) e 107 Chapter 8: Application Examples Program code Key operations If S<100 Goto AGAIN i 8 ; S i D 100 ; s i 9 @ a AGAIN ; e S=S˚10^(-3) ; S ; = ; S k @ Y ( S 3 ) e If N>6 Goto SIX i 8 ; N i G 6 ; s i 9 @ a SIX ; e If N>3 Goto THREE i 8 ; N i G 3 ; s i 9 @ a THREE ;e Q=ipart(Sx10^N) ; Q ; = I 1 ( ; S k @ Y ; N ) e Goto DISPLAY i 9 @ a DISPLAY ; e Label SIX i 6 @ a SIX ; e Q=ipart(S˚10^(N-6))˚10^6 +random˚10^6+random˚10^3 ; ; + Y @ Q ; = I 1 ( S k @ Y( ; N 6 ) ) k @ Y 6 @ w 0 k @ 6 + @ w 0 k Y 3 e Goto DISPLAY i 9 @ a DISPLAY ; e Label THREE i 6 @ a THREE ; e Q=ipart(S˚10^(N-3))˚10^3 +random˚10^3 ; ; + Y Q ; = I 1 ( S k @ Y( ; N 3 ) ) k @ Y 3 @ w 0 k @ 3 e Label DISPLAY i 6 @ a DISPLAY ; e Clrt i 7 e Print Q i 0 ; Q e 108 Chapter 8: Application Examples Program code Key operations Wait T i 3 ; T e Clrt i 7 e Print”ANSWER i 1 @ a ANSWER ; e Input X i 2 ; X e * If answer is correct, add (30 x number of digits / number of seconds) to score. If X Q Goto WRONG i 8 ; X i H ; Q ; s i 9 @ a WRONG ; e A=A+int(10˚N©T˚3) ; A ; = ; A + I 2 ( 10 k ; N z ; T k 3 ) e Label WRONG i 6 @ a WRONG ; e M=M+1 ; M ; = ; M + 1 e If M<=10 Goto QUESTION i 8 ; M i E 10 ; s i 9 @ a QUESTION ; e Print”YOUR SCORE IS i 1 @ a YOUR s SCORE s IS ; e Print A i 0 ;A e End i 5 e Running the program 4. Press j to return to the PROG mode menu. 5. Press 0, select the program ‘NUMBER’ and press e. 6. Enter the number of digits you wish to play with N. 7. Enter the number of seconds to display the numbers. 8. Immediately after you press e, the game will start. 9. After ‘ANSWER X=?’ is displayed, enter the number you remembered and press e. After 10 tries, the score is displayed. 109 Chapter 8: Application Examples Calculation Examples Geosynchronous orbits The orbit of a satellite about the Earth is geosynchronous if the period of the orbit matches the period of the Earth’s rotation. At what distance from the center of the Earth can geosynchronous orbit occur? The period of an orbit is described by the equation 4π2 r3 T2 = —— GM where T = period of orbit G = Gravitational constant (6.6742 × 10–11 m3 kg–1s–2) M = Mass of the Earth (5.976 × 1024 kg) r = Distance between the satellite and the center of the Earth (radius of orbit) The Earth rotates once every 23 hours, 56 minutes and 4.09 seconds. At first, convert this time into seconds. Press b 0 23 [ 56 [ 4.09 [ I 6. 1. • Determining the value of T. 23∂56∂4.09∂Ωse c 86164.09 Press x T to store the result as global variable T. 2. Press @ J 1 1 4. 3. • Select the scientific display format with four significant digits. 86164.09 AnsÒT 8.616 • Use the solver function to solve the equation for r. 4. Press j ; T A ; = (4@sA)z( ; G ; M ) k ; R 1. 5. Check the equation on the display and press I 5 to enter the solver function. 110 0.000 TŒ=(4πŒ)©(GM)˚ R„_ TŒ=(4πŒ)©(GM)˚ R„ G=z 0.000 Chapter 8: Application Examples 6. Press @ c 02 e 5.976 ` 24 e. • Use the physical constants function for the G value. TŒ=(4πŒ)©(GM)˚ R„ R=z 0.000 • After completion of entering values for variables G and M, the cursor moves on to variable R. (The variable T has already its value.) 7. Press @ h. Result Geosynchronous orbit is possible approximately 42,170 km (4.217 × 107 meters) from the center of the Earth. R= R¬ L¬ 4.217 7.424 7.424 Twinkle, twinkle, little star (Apparent magnitude of stars) The apparent magnitude of a star is a measure of how bright it appears. It is a function of how far away the star is and the luminosity of the star. Since stars are seen from different distances, their luminosities must be standardized before they can be compared. This is done using a quantity called the absolute magnitude, which is a measure of how bright that star would appear if it was viewed from a distance of 10 parsecs (about 32.6 light years). If the absolute magnitude of two stars is known, the ratio of their luminosities is given by the equation. L2 Log —— = 0.4 (M1 – M2) L1 where M1 = Absolute magnitude of the first star M2 = Absolute magnitude of the second star L1 = Luminosity of the first star L2 = Luminosity of the second star 111 Chapter 8: Application Examples Example 1 What is the ratio of the sun’s luminosity to that of a star having an absolute magnitude of 2.89? (The sun’s absolute magnitude is 4.8.) The former equation is equivalent to L2 —— = 10 0.4 (M1 – M2) L1 whereM2 = 2.89 1. Press b 0 and @ P 0. 2. Press @ Y ( 0.4 k ( 4.8 - 2.89 ) ) e. Result 1Î^(0.4˚(4.8-2. 89))= 5.807644175 5.807644175 The star is nearly six times as luminous as the sun. Example 2 A second star has only 0.0003 times the luminosity of the sun. What is its absolute magnitude? The previous equation is equivalent to L2 log —— L1 M2 = M1 – ———— 0.4 L2 where —— = 0.0003 L1 1. Press 4.8 - ( l 0.0003 z 0.4 ) e. Result The absolute magnitude of the second star is approximately 13.6. 112 4.8-(log0.0003 ©0.4)= 13.60719686 Chapter 8: Application Examples Memory calculations When you want to use the calculator for tasks such as adding up total sales, you can perform this type of operation using single-variable statistics. Example In one week, an electrical store sold the items listed below at the prices and in the quantities shown. What was the total sales figure? Item TV set Price $599.95 Quantity 10 Phone $159.95 27 Clock $39.95 52 Calculator $7.95 108 1. Press b 1 0 to select the single-variable statistics mode. 2. Press 599.95 , 10 _, 159.95 , 27 _, 39.95 , 52 _ and 7.95 , 108 _. DATA SET= 3. 7.95,108DATA DATA SET= 4. • All the data is entered. 3. Press I 0 4 e. • The calculator displays Σx, that is the total sales value. DATA SET= 4. Í≈= 13254.15 Result ■ Total sales were $13254.15. 113 Chapter 8: Application Examples The state lottery Example The state you live in has two different numbers lotteries. In the first, you must pick 6 numbers between 1 and 50 in any order. In the second, you have to pick 5 numbers between 1 and 35, but you must pick them in the correct order. Which lottery gives you the better chance of winning? In the first lottery, your chances of winning with one ticket are one in 50C6: 1. Press b 0 50 @ N 6 e. 0. 50Ç6= 15890700. Your chances of winning the second lottery with one ticket are one in 35P 5 : 2. Press 35 @ e 5 e. Result ■ Your chances are better in the first lottery. 114 15890700. 35∏5= 38955840. Appendix Battery Replacement Batteries used • Use only the specified batteries. Type Model Quantity Lithium battery CR2032 2 • Be sure to write down any important data stored in the memory before replacing the batteries. Notes on battery replacement Improper handling of batteries can cause electrolyte leakage or explosion. Be sure to observe the following handling rules: • • • • Do not mix new and old batteries. Make sure the new batteries are the correct type. When installing, orient each battery correctly as indicated in the calculator. Batteries are factory-installed before shipment, so may become exhausted before reaching the service life stated in the specifications. When to replace the batteries Replace the batteries immediately when any of the following situations occur: • The calculator does not turn on when j is pressed. • The message ‘Change Batteries’ appears. • Continued use of the calculator when in low battery status may result in the memory contents being cleared. • Executing programs under low battery condition may result in the memory contents being cleared. • Failure to follow the battery replacement procedure as described may result in the memory contents being cleared. 115 Appendix Cautions • Fluid from a leaking battery accidentally entering an eye could result in serious injury. Should this occur, wash with clean water and immediately consult a doctor. • Should fluid from a leaking battery come in contact with your skin or clothes, immediately wash with clean water. • If the product is not to be used for some time, to avoid damage to the unit from leaking batteries, remove them and store in a safe place. • Do not leave exhausted batteries inside the product. • Do not fit partially used batteries, and be sure not to mix batteries of different types. • Keep batteries out of the reach of the children. • Exhausted batteries left in the calculator may leak and damage the calculator. • Explosion risk may be caused by incorrect handling. • Do not throw batteries into a fire as they may explode. Replacement procedure • All memory contents will be cleared if you remove both batteries at the same time. Always replace each battery before removing the other one. • Make sure the power is turned off before replacing the batteries. • Do not press j until the battery replacement procedure is complete. 1. Turn the power off by pressing @ o. 2. Remove the two screws. 3. Lift the battery cover to remove. 116 Appendix 4. Remove one used battery by prying it out with a ball-point pen or similar pointed object. • Replace one battery at this step. 5. Install a new battery with the positive side (+) facing up. 6. Repeat steps 4 and 5 to replace the other battery. 7. Replace the cover and screws. 8. Press the RESET switch using the tip of a ball-point pen or similar object. • If you cannot see the message on the right, repeat steps 1–7. 9. zALL DATA CL?z z YES¬[DEL] z z NO¬[ENTER]z Press e. • Do not press y. If y is pressed, the memory contents will be cleared. 10. Adjust the LCD contrast. (See page 118.) Automatic power off function The calculator will turn itself off to save battery power if no key is pressed for approximately 10 minutes. 117 Appendix The OPTION menu The OPTION menu controls display contrast, memory checking and deletion of data. The OPTION display Press @ o (S key) to show the OPTION menu. • Press j to return to the mode in which you were working previously. <OPTION> ƒCTRST ⁄M.CHK ¤DELETE Contrast Press 0 in the OPTION menu to show the LCD CONTRAST display. • Press + to darken the display and - to lighten it. LCD CONTRAST [+] [-] DARK® ¬LIGHT • It is possible to lighten the display so much that the calculator appears to be off. If the display remains blank when you press X, press @ o 0 and then press + repeatedly to darken the display. Memory check Press 1 in the OPTION menu to show the MEMORY CHECK display. • The amount of free memory in bytes is shown on the first line. When the calculator is used for the first time, the following amount of memory is available. 624BYTES FREE EQTN: 15 PROG: 09 [EL-5250] 4,096 bytes [EL-5230] 1,280 bytes • The figures after EQTN are the numbers of equations (Filing equations functions) in the NORMAL mode. • The figures after PROG are the numbers of programs stored in the PROG mode. For a detailed description of how memory is used, refer to ‘Memory usage’. (See page 126.) 118 Appendix Deleting equation files and programs Press 2 in the OPTION menu to show the DELETE menu. • Press 0 or 1 to delete equation files or programs that have been stored in the NORMAL or PROG modes, respectively. <<DELETE>> ƒEQTN ⁄PROG After selecting the mode for which data is to be deleted, press y to delete data. Press e to cancel the operation. • Once a file has been deleted there is no way to recover it. To delete individual files, enter the mode that contains the data you want to delete and use the specific delete function from the menu. (See pages 59 and 86.) If an Abnormal Condition Occurs Should an abnormal condition occur, such as none of the keys (including j) functioning, press the RESET switch located on the back of the calculator. Refer to page 32. 119 Appendix Error Messages The following table shows common error messages and suggestions for correcting the error. Error no. Solution SYNTAX Verify you are using the correct syntax for the function you are trying to apply. 02 CALCULATION Check you have not attempted to divide by zero or made some other calculation error. 03 NESTING Use of more than the available number of buffers was attempted. (There are 10 buffers* for numeric values and 24 buffers for calculation instructions.) * 5 buffers in the CPLX mode. 04 LBL DUPLICATE Make sure your program does not use the same label name to specify more than one location. 05 LBL UNDEFINED Make sure your program does not have a Goto or Gosub command pointing to a label that does not exist. Note that you can include labels that are not pointed to by Goto or Gosub commands without affecting program operation. 06 LBL OVER Make sure your program does not have more than 20 labels. 07 GOSUB STACK Make sure your program does not have more than 10 levels of nested subroutines. 08 CAN’T RETURN Make sure your program does not have a Return command with no corresponding Gosub command. 09 MEMORY OVER Not enough free memory remains for what you are trying to do. Delete unneeded files and try again. 10 STORAGE FULL Make sure the maximum number of 99 saved equations or 99 programs is not exceeded. Delete unneeded equations or programs and try again. 11 DATA OVER Use of more than 100 data items in the STAT mode was attempted. The maximum number of 160 characters in the equation input buffer was exceeded. BREAK! You have pressed j to stop a program or solver calculation. (No number) 120 Error message 01 Appendix Using the Solver Function Effectively The calculator uses Newton’s method to solve equations. (See page 52.) Because of this, the solution it provides may differ from the true solution, or an error message may be displayed for a soluble equation. This section shows how you can obtain a more acceptable solution or make the equation soluble in such cases. Newton’s method Newton’s method is a successive approximation technique that uses tangential lines. The calculator chooses an ‘approximate’ solution then calculates and compares the right-hand and lefthand sides of the equation. Based on the result of this comparison, it chooses another ‘approximate’ solution. It repeats this process until there is hardly any discrepancy between the right-hand and left-hand sides of the equation. y = f(x) y Tangential lines Solution x Initial value Newton’s method Intersections of dotted lines with the x-axis give successive approximate solutions found using Newton’s method. ‘Dead end’ approximations When @ h is pressed for the first time, the calculator takes the value that is stored in memory, or zero if no value is stored, to be the initial expected value for the unknown variable and tries to solve the equation. If it fails to find an acceptable solution using this expected value, it tries again using up to nine more initial expected values until a solution is found. If none of the values lead by successive approximation toward an - ERROR 02 acceptable solution — but rather to a ‘dead CALCULATION end’ — the calculator will abort calculation and display an error message. Range of expected values After the stored value (or zero) has been tried, new initial expected values are selected according to the range of expected values for the equation. (See ‘Changing the range of expected values’.) To choose which initial expected values to try, the calculator divides the range into eight subranges of equal width and tries each of the values at the edges of these subranges in turn (starting with the lower limit of the range of expected values, a). 121 Appendix Calculation accuracy • The calculator solves an equation by comparing the values of the lefthand and right-hand sides of the equation through 14-digit internal operations. If the value of the left-hand side is sufficiently close to agreeing with that of the right-hand side the calculator may present one of the ‘approximate’ values as a solution — even though it is not the true solution. • The calculator will also stop trying to solve an ‘approximate’ solution either when it has performed more than 50 iterations using each initial expected value or when it has obtained an ‘approximate’ solution that is the same (to 10-digit accuracy) twice in succession. Changing the range of expected values After entering your equation by pressing I 5, press @ J to adjust the range of expected values. The calculator will then prompt you for a range of expected values (between –1 × 1099 and +1 × 1099) to be used in the calculation. RANGE:a<b a= –1. b= 1. a: Lower limit b: Upper limit • The range of expected values returns to its default setting (–1 × 1010 to +1 × 1010) when the current equation is cleared or the mode is changed. After entering the lower and upper limits (a and b) of the range of expected values, press j to return to the previous display. • The best solution can be found by defining the lower or upper limit (a or b) or initial value close to the expected solution. • Having done this, press @ h several times to generate slightly different solutions. You can judge which of these is the best by comparing the values displayed for the left-hand and right-hand sides of the equation. 122 Appendix Equations that are difficult to solve Newton’s method has problems in solving certain types of equations, either because the tangential lines it uses to approximate the solutions iterate only slowly toward the correct answer, or because they do not iterate there at all. Examples of such equations include equations of which steep slopes are a feature (e.g. y = 10x–5), periodic functions (e.g. y = sin x), functions featuring an inflection (e.g. y = x3–3x2 + x + 5) and functions where the unknown variable appears as a denominator (e.g. y = 8/x + 1). y x Solving y =10x – 5 for y = 0. Because of the steep slope, it takes a long time to iterate to the correct solution. Set limits a and b as close as possible either side of your expected solution. Many of those equations may become soluble if a range of expected values is defined that corresponds closely to the real solution. • For periodic functions such as sin x and cos x, the gradient near peaks or troughs is very shallow. If the initial expected value falls too close to a peak or trough, the calculator may iterate to a totally different cycle of the function and will not obtain an accurate solution. Make sure the initial expected value is an appropriate distance between a peak and a trough. • Where appropriate, you can try rearranging the equation so that the unknown variable is no longer a denominator. Solving y = sin x for y = 0. If the Initial expected value is too close to a peak, the calculator will iterate away from the correct solution. y x Solving y = x3 – 3x2 + x + 5 for y = 0. If the initial expected value is x = 3, no solution is obtained. However, setting x to –3 gives the correct solution of –1. 123 Appendix Technical Data Calculation ranges • Within the ranges specified, the calculator is accurate to ±1 of the least significant digit of the mantissa. However, in continuous calculations the calculation error increases due to the accumulation of each successive calculation error. (This is the same for yx, x , n!, ex, In etc., where continuous calculations are performed internally.) • Furthermore, the calculation error will accumulate and become larger in the vicinity of inflection points and singular points of functions, and in programmed repetitive calculations. • Calculation ranges ±10-99 to ±9.999999999 × 1099 and 0. If the absolute value of an entry or a final or intermediate result of a calculation is less than 10-99, the value is considered to be 0 in calculations and on the display. Function Dynamic range DEG: sin x, cos x, tan x RAD: | x | < 1010 (tan x : | x | =/ 90 (2n–1))* π | x | < —– × 1010 180 π (tan x : | x | =/ — (2n–1))* 2 10 × 1010 GRAD: | x | < —– 9 (tan x : | x | =/ 100 (2n–1))* sin–1x, cos–1x tan–1x, 3√x In x, log x yx |x|≤1 | x | < 10100 10–99 ≤ x < 10100 • y > 0: –10100 < x log y < 100 • y = 0: 0 < x < 10100 • y < 0: x = n 1 (0 < l x l < 1: — = 2n–1, x =/ 0)*, x –10100 < x log | y | < 100 1 x • y > 0: –10100 < — log y < 100 (x =/ 0) x __ √y • y = 0: 0 < x < 10100 • y < 0: x = 2n–1 1 (0 < | x | < 1 : — = n, x =/ 0)*, 1 x x –10100 < — log | y | < 100 124 Appendix Function ex 10x sinh x, cosh x, tanh x sinh–1 x cosh–1 x tanh–1 x x2 x3 __ √x x–1 n! nPr nCr Dynamic range –10100 < x ≤ 230.2585092 –10100 < x < 100 | x | ≤ 230.2585092 | x | < 1050 1 ≤ x < 1050 |x|<1 | x | < 1050 | x | < 2.15443469 × 1033 0 ≤ x < 10100 | x | < 10100 (x ≠ 0) 0 ≤ n ≤ 69* 0 ≤ r ≤ n ≤ 9999999999* n! —— < 10100 (n-r)! 0 ≤ r ≤ n ≤ 9999999999* 0 ≤ r ≤ 69 n! —— < 10100 (n-r)! ↔DEG, D°M’S 0°0’0.00001” ≤ | x | < 10000° x, y → r, θ x2 + y2 < 10100 0 ≤ r < 10100 DEG: | θ | < 1010 r, θ → x, y DRG (A+Bi)+(C+Di) (A+Bi)–(C+Di ) (A+Bi) ×(C+Di) (A+Bi)÷(C+Di) π 180 10 GRAD : | θ | < — × 1010 9 RAD: | θ | < —– × 1010 DEG→RAD, GRAD→DEG: | x | < 10100 π 2 RAD→GRAD: | x | < — × 1098 | A + C | < 10100, | B + D | < 10100 | A – C | < 10100, | B – D | < 10100 (AC – BD) < 10100 (AD + BC) < 10100 AC + BD < 10100 C2 + D2 BC – AD < 10100 C2 + D2 C2 + D2 =/ 0 125 Appendix Function →DEC →BIN →PEN →OCT →HEX AND OR XOR XNOR Dynamic range DEC : | x | ≤ 9999999999 BIN : 1000000000 ≤ x ≤ 1111111111 0 ≤ x ≤ 111111111 PEN : 2222222223 ≤ x ≤ 4444444444 0 ≤ x ≤ 2222222222 OCT : 4000000000 ≤ x ≤ 7777777777 0 ≤ x ≤ 3777777777 HEX : FDABF41C01 ≤ x ≤ FFFFFFFFFF 0 ≤ x ≤ 2540BE3FF : 1000000000 ≤ x ≤ 1111111111 0 ≤ x ≤ 111111111 PEN : 2222222223 ≤ x ≤ 4444444444 0 ≤ x ≤ 2222222221 OCT : 4000000000 ≤ x ≤ 7777777777 0 ≤ x ≤ 3777777777 HEX : FDABF41C01 ≤ x ≤ FFFFFFFFFF 0 ≤ x ≤ 2540BE3FE BIN : 1000000001 ≤ x ≤ 1111111111 0 ≤ x ≤ 111111111 PEN : 2222222223 ≤ x ≤ 4444444444 0 ≤ x ≤ 2222222222 OCT : 4000000001 ≤ x ≤ 7777777777 0 ≤ x ≤ 3777777777 HEX : FDABF41C01 ≤ x ≤ FFFFFFFFFF 0 ≤ x ≤ 2540BE3FF BIN NOT NEG * n, r: integer Memory usage The amounts of memory the calculator uses for variables, programs and equations are shown below. Variables Each variable uses 1 byte, and each local variable uses 9 bytes to store its value. Programs Creating a new program uses 32 bytes of memory irrespective of the length of its name. Each line in a program uses 3 bytes plus the number of characters or commands on the line (each character or command uses 1 byte). For example, the two lines of the program shown below use 60 bytes. 126 Appendix Management Characters, commands and variables For value of local variables Total Program title If A=0 Goto ABC A¡=A+1 32 bytes 3 bytes 3 bytes — 8 bytes 5 bytes — — 9 bytes 32 bytes 11 bytes 17 bytes Total consumption 38 bytes 13 bytes 9 bytes 60 bytes Filing Equation functions Each stored equation uses 30 bytes plus the number of characters or commands. Priority levels in calculations Operations are performed according to the following priority: Fractions (1ı4, etc.) ∠ , engineering prefixes Functions preceded by their argument (x−1, x2, n!, etc.) Yx , x Implied multiplication of a memory value (2Y, etc.) Functions followed by their argument (sin, cos, (–), etc.) Implied multiplication of a function (2sin30, etc.) nCr, nPr ×, ÷ +, − AND OR, XOR, XNOR =, M+, M−, ⇒M, 왘DEG, 왘RAD, 왘GRAD, DATA, CD, →rθ, →xy, and other calculation ending instructions • If parentheses are used, the parenthesized calculations have precedence over the other calculations. 127 Appendix Specifications Model: EL-5230/5250 Display type: [14 characters and 2 exponents] × 3 rows Dot matrix characters: 5 × 7 dots /character Number of display digits: 10-digit mantissa + 2-digit exponent Input ranges: ±10-99 to ±9.999999999 × 1099 and 0. (up to 10-digit mantissa) Number of internal calculation digits: 14-digit mantissa Pending operations: 24 calculations 10 numeric values (5 numeric values in the CPLX modes) Calculation functions: Calculations (four basic arithmetic operations, calculations with parentheses, memory calculations, function calculations, etc.), differential/integral functions, binary/ pental/octal/decimal/hexadecimal operations, solver functions, simulation calculations, complex number calculations, etc. Statistical calculations: One-variable statistics, two-variable statistics, normal probability calculations, etc. Equation solvers: Simultaneous linear equations, and quadratic/cubic equation solvers. Programming function: New programming, running a program, and editing a program and deleting a program. Option menu: LCD contrast, memory check and data deletion Memory capacity: [EL-5250] 4,096 bytes (user area) [EL-5230] 1,280 bytes (user area) Power source: 3 V (DC): Lithium battery (CR 2032) × 2 Auto power off: After approximately 10 minutes Power consumption: 0.002 W Operating temperature: 0°C – 40°C (32°F – 104°F) Operating time: Approximately 1,800 hours* (at 25°C (77°F), assuming each hour consists of 5 minutes of continuous operation and 55 minutes of display time). 128 Appendix Dimensions: 79.6 mm (W) × 154.5 mm (D) × 15.2 mm (H) 3-1/8” (W) × 6-3/32” (D) × 19/32” (H) Weight: Approx. 97 g (0.22 lb) (including batteries, but not including hard case) Accessories: 2 lithium batteries (installed), operation manual, quick reference card and hard case * This value may vary according to the way the calculator is used and other factors. For More Information about Scientific Calculators Visit our Web site. http://sharp-world.com/calculator/ In Europe: This equipment complies with the requirements of Directive 89/336/EEC as amended by 93/ 68/EEC. Dieses Gerät entspricht den Anforderungen der EG-Richtlinie 89/336/EWG mit Änderung 93/ 68/EWG. Ce matériel répond aux exigences contenues dans la directive 89/336/CEE modifiée par la directive 93/68/CEE. Dit apparaat voldoet aan de eisen van de richtlijn 89/336/EEG, gewijzigd door 93/68/EEG. Dette udstyr overholder kravene i direktiv nr. 89/336/EEC med tillæg nr. 93/68/EEC. Quest’ apparecchio è conforme ai requisiti della direttiva 89/336/EEC come emendata dalla direttiva 93/68/EEC. 89/336/, 93/68/ . Este equipamento obedece às exigências da directiva 89/336/CEE na sua versão corrigida pela directiva 93/68/CEE. Este aparato satisface las exigencias de la Directiva 89/336/CEE modificada por medio de la 93/68/CEE. Denna utrustning uppfyller kraven enligt riktlinjen 89/336/EEC så som kompletteras av 93/68/ EEC. Dette produktet oppfyller betingelsene i direktivet 89/336/EEC i endringen 93/68/EEC. Tämä laite täyttää direktiivin 89/336/EEC vaatimukset, jota on muutettu direktiivillä 93/68/ EEC. Ñ‡ÌÌÓÂ ÛÒÚÓÈÒÚ‚Ó ÒÓÓÚ‚ÂÚÒÚ‚ÛÂÚ ÚÂ·Ó‚‡ÌËﬂÏ ‰ËÂÍÚË‚˚ 89/336/EEC Ò Û˜ÂÚÓÏ ÔÓÔ‡‚ÓÍ 93/68/EEC. Ez a készülék megfelel a 89/336/EGK sz. EK-irányelvben és annak 93/68/EGK sz. módosításában foglalt követelményeknek. Tento pﬁístroj vyhovuje poÏadavkÛm smûrnice 89/336/EEC v platném znûní 93/68/EEC. 129 EL-5230/EL-5250 04LGK (TINSE0796EHZZ) PRINTED IN CHINA / IMPRIMÉ EN CHINE / IMPRESO EN CHINA PROGRAMMABLE SCIENTIFIC CALCULATOR SHARP CORPORATION ® EL-5230 EL-5250 PROGRAMMABLE SCIENTIFIC CALCULATOR OPERATION MANUAL

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