FRIDEN MODEL 1155 ADVANCED PROGRAMMABLE CALCULATOR SINGER

FRIDEN  MODEL  1155 ADVANCED  PROGRAMMABLE CALCULATOR SINGER
REFERENCE MANUAL
FRIDEN MODEL 1155
ADVANCED PROGRAMMABLE
CALCULATOR
SINGER
BUSINESS MACHINES
WILLIAM R. "PALLiSCHI
REFERENCE MANUAL
FRIDEN MODEL 1155
ADVANCED PROGRAMMABLE
CALCULATOR
Publication No. 55-538
September, 1972
SINGER
BUSINESS MACHINES
2350 WASHINGTON AVE
SAN LEANDRO. CALIF. 94577
Copyright © 1972. The Singer Company
All rights reserved throughout the world.
PRINTED IN U.S.A.
LIST OF EFFECTIVE PAGES
Effective Date
Page
i thru vi
1-1 thru
2-1 thru
3-1 thru
4-1 thru
A-1 thru
B-1 thru
1-1 thru
9/72
1-4
2-36
3-30
4-8
A-2
B-3
I-3
9/72
9/72
9/72
9/72
9/72
9/72
9/72
9/72
Model 1155 Reference Manual
iii
CONTENTS
Page
1
2
3
4
9/72
INTRODUCTION
1-1
Modes
1-2
Registers
1-3
Program Memory
1-3
Program Codes
1-4
Error Messages
1-4
KEYBOARD OPERATIONS
2-1
Keyboard Mode Keys
2-1
Input/Output
2-1
Binary Operation Keys
2-11
Function Keys.
2-17
Memory Registers
2-31
3-1
PROGRAMMING
Stored Programs and Programming Modes
3-1
Abbreviations for Instructions Discussed in Section 2 .
3-1
Sample Program
3-5
Write Mode
3-6
List Mode
3-7
Run Mode
3-10
Program Code and Go To
3-12
Magnetic Card Reader
3-26
Fractional Part of X .
3-28
Cube Root
3-28
Signum Function
3-29
Modulus Function
3-30
EDITING A PROGRAM'
4-1
Insert Mode
4-1
Delete Mode
4-2
Checksums
4-7
Model 1155 Reference Manual
v
Contents
Page
APPENDIX A - FUNCTION KEYS
Summary .
APPENDIX B - MISCELLANEOUS PROCEDURES
A-1
B-1
Loading Paper Tape
B-1
Changing Ink Roller
B-2
INDEX·
vi
A-1
Model 1155 Reference Manual
1-1
9/72
1
INTRODUCT ION
The Friden* 1155 is a programmable calculator with the following fea tures:
•
It may be usefl as an ordinary desktop calculator; many operations may
be performed directly from the keyboard with no programming required.
to 10 99 .
•
13 digit accuracy in the range 10 -
•
Printing in either fi)\ed point or scientific notation.
•
Programming either from the keyboard or with the Model 511 magnetic
card reader, of up to 511 program steps .
•
Easy insertion and deletion of program steps.
•
Progr a m listing.
•
Two working registers and twenty memor y registers.
•
Up to 100 program codes (labels).
•
Indirect addressing of register s and program codes.
•
Full complement of arithmetic and mathematical functions.
99
Friden 1155 Programmable Calculator
*A trademark of The Singer Company
9/72
Model 1155 Reference Manual
1-1
Introduction
MODES
The 1155 may be in any of seven states or modes. The central mode, called the
keyboard mode, may be reached at any time from any of the other modes by
pressing RESET.
The following is a brief description of each mode. Greater detail is available in
the associated sections of this manual.
KEYBOARD MODE
Allows the user to directly operate all arithmetic and mathematical functions
and to input numbers and print answers. All other modes are reached via the
keyboard mode.
PROGRAMMING MODES
Write Mode
Allows the user to enter programs into the 1155's program memory
from the keyboard.
Run Mode
Runs programs entered either from the keyboard or from the Model 511
magnetic card reader.
List Mode
Allows the user to list the program in the program memory, entirely
or one step at a time, to print a checksum, or to print the number of
unused program steps.
CARD READER CONTROL MODE
Allows the user to enter programs into the program memory from the Model 511
magnetic card reader, and to store programs onto magnetic cards from the
program memory.
EDITING MODES
Insert Mode
Allows the user to insert new steps in the stored program.
Delete Mode
Allows the user to delete steps from the stored program.
1-2
Model 1155 Reference Manual
9/72
Introduction
REGISTERS
Numbers are stored in registers.
There are
2 WORKING REGISTERS
20 MEMORY REGISTERS
Each register can store one number at a time.
Working Registers
The two working registers in the 1155 are thought of as being "stacked" one on
top of the other. For this reason they are named Lower, abbreviated L, and
Upper, abbreviated U.
All numeric operations are done with the working registers, with the single exception of ACCUMULATE STORE which operates on L and a memory register.
Numeric operations are divided into two groups called unary and binary operations. Unary operations affect only the L register. An example of a unary
operation is CHANGE SIGN. Binary operations affect both Land U. The result
is put into L, and U is cleared (set to zero). Examples of binary operations
are addition and multiplication.
Memory Registers
The twenty memory registers in the 1155 are numbered 00 through 19.
registers may be used to store numbers.
These
Numbers are transferred from L to the memory registers using STORE, and
from the memory registers to L using RECALL. All memory registers may be
cleared (set to zero) using CLR REG.
In addition, memory register 00 may be used to address other registers in
conjunction with the INDIRECT key. Otherwise, register 00 behaves exactly
like memory registers 01 through 19.
PROGRAM MEMORY
The program memory stores program instructions in the order they are entered.
The maximum number of single key instructions is 511; since some instructions
require two or more keystrokes (e.g., GO TO INDIRECT), the maximum number
of instructions will generally be less than 511.
9/72
Model 1155 Reference Manual
1-3
Introduction
PROGRAM CODES
A program may contain up to 100 program codes, which are two-digit numbers
identifying places in a program to be used as entry points (for example, in program loops, subroutines, etc.). Program codes are numbered 00 through 99.
ERROR MESSAGES
When an error (overflow, argument outside the range of a function, division by
zero, undefined term, and so on) is encountered in keyboard, list or running
modes, the 1155 prints an ERROR message. The table below lists all error
messages with brief explanations.
ERROR
1
Exponent in eX or I A Ix positive and large enough to create
an answer greater than 10 1 0 0.
2
The absolute value of the tangent of the angle specified is
greater than 10 10
3
Attempt to compute logarithm of zero.
4
1-4
EXPLANA TION
°.
Attempt to compute ARC SIN or ARC COS of x for which
Ix 1>1.
5
Division by zero.
6
Attempt to compute I x I ! for Ix I~100.
7
Exponent of normalized answer greater than 99 or I x I !
where 69 < Ixl < 100.
8
Attempt to compute reciprocal of zero.
9
Illegal key entry during manual operation.
10
Attempt to compute polar coordinates when rectangular
coordinates are both zero (x = 0, y = 0).
11
Incomplete address during list.
12
Incorrect indirect address in REG 00 or incorrect indirect
address key sequence.
Model 1155 Reference Manual
9/72
2
KEYBOARD OPERATIONS
The ON-OFF switch is located underneath the right side of the 1155.
1155 is turned ON:
When the
•
It is in keyboard mode.
•
It is set to two-decimal place printout.
•
The print wheel spins.
•
Working registers Land U are set to zero.
•
Angles are set to read in degrees and the DEG key light comes on.
e
It prints f .00'.
KEYBOARD MODE KEYS
Keyboard mode is the central, "normal" mode of operation. All other modes
are reached only through the keyboard mode. In this mode, direct operation of
the number entry. printer, arithmetic, memory register and function keys is
a vailable to the user.
Clears both working registers,L and U. Does not clear
memory registers or program memory. Returns the 1155
to KEYBOARD MODE from all other modes; for this reason
the RESET key may be used to terminate an unknown or undesirable state (for example, an infinite loop in a program).
Pressing RESET causes the print wheel to spin and a line
space to be printed.
INPUT /OUTPUT
The following keys are used when entering numbers into the 1155 or printing
numbers on the printer.
CLEAR
ENTRY
ENTER
EXPONENT
7
8
9
4
5
6
.1
2
3
CHANGE
SIGN
[W
ET
DEC
(
)
LINE
SPACE
9/72
Model 1155 Reference Manual
2-1
Keyboard Operations
Terminates entry of a number and causes it to be printed.
In the following examples it is assumed that the number of decimal places for
printout has been set to 2. Press RESET ..
•
•
•
Enter 123
[J0G EJ
PRINTOUT
1.23.00
Enter 123.45
00GD808
1.23.45
Enter .37 (two ways are shown)
DGJ0 EJ
DGJ8 B
.37
.37
When a number is keyed in:
2 -2
•
The previous content of L (Lower register) is transferred to U (Upper
register).
•
The number being entered is placed in L.
•
The previous content of U is lost.
Model 1155 Reference Manual
9/72
Keyboard Operations
The following example records the contents of Land U as successive numbers
are entered. The number of decimal places for printout is set to 2.
KEYS
L
U
EJ
0
0
25
0
25.00
7
25
7.00
30
7
30.00
99
30
99.00
[J GB
[J 8
0G8
~GB
PRINTOUT
A number may contain up to 13 Significant digits. All digits (up to 13) are stored
in L. However, the printout is rounded to the number of decimal places set for
printout. For example, assume that the number of places for printout is set to 2.
KEYS
9/72
L
PRINTOUT
Ju234
:lJ.23
:lJ.235
:lJ.24
--------------------------------------
.0379
.04
.0049
.00
Model 1155 Reference Manual
2-3
Keyboard Operations
CHANGE
SIGN
Changes the sign of the number being entered.
In the following examples the printout is set for two decimal places.
•
PRINTOUT
Enter -123
000
•
8
-1.23.00
CHANGE
SIGN
8
-5.90
Enter -5.9
0DG
•
CHANGE
SIGN
Enter -.375
DGCJO
•
CHANGE
SIGN
8
-.38
Enter -.0023
DGG0G
CHANGE
SIGN
8
-.00
In the last example, the 1155 printed "negative zero" because the number of
decimal places for printout was set to 2. The number is correctly stored in L
as -.0023, however.
In the above examples, the CHANGE SIGN key is pressed after entering the last
digit of the number. Actually, it may be pressed anytime during entry. For
example:
•
Enter -123
CHANGE
SIGN
2-4
Model 1155 Reference Manual
-:123.00
9/72
Keyboard Operations
Internally, numbers are stored in scientific notation. In scientific notation, a
number is represented by a mantissa and an exponent. For example, the
number 123.45 is represented as follows.
1.2345
X
10 2 --exponent
mantissa~
In the 1155, a number is represented by a 13 digit mantissa and a two digit exponent. The following table indicates how certain numbers are represented in the
1155.
NUMBER
EXPONENT
MANTISSA
123.45
1.234500000000
+02
.0023
2.300000000000
-03
-:1234567
-:1.234567000000
+23
6.02 x 10 23
6.020000000000
+06
9 x 10 99
9.000000000000
+99
1 x 10- 99
:1.000000000000
-99
The 1155 can operate on numbers with up to 13 significant digits in the following ranges:
ZERO:
1. 000000000000X:10- 99
to 9. 999999999999X:10 99
NEGATIVE NUMBERS: -1. 000000000000X:10- 99
to-9. 999999999999X:10 99
POSITIVE NUMBERS:
9/72
Model 1155 Reference Manual
2-5
Keyboard Operations
i
PRIN
SCI
Terminates entry of a number and causes the number to be printed in
scientific notation. The mantissa is rounded to 12 significant digits and
the letter "E" is printed between the mantissa and the exponent.
1
•
Enter 123.45 and print in scientific notation.
~.23450000000E+02
•
Enter .0023 and print in scientific notation.
2.30000000000E-03
•
•
Enter 7 and print in scientific notation.
Gli
u
PRINT
SCI
I
7.00000000000E+OO
Enter 0 and print in scientific notation.
I
RESET
II
PRINT
SCI
I
[
o
]
The following illustrates the entry of negative numbers followed by a printout
in scientific notation.
•
Enter -123
~ r;l r-;-l
UUU
•
•
IPRINT
I
SCI
Enter -5.9
r--;lDI;l
LJ
LJ
•
CHANGE
SIGN
Enter -.375
CHANGE [PRINT[
SIGN
. SCI
D GJ 00 C~~~~E IP~~~T I
-5.90000000000E+OO
-
-
-3.75000000000E-O~
-
Enter -.0023
-2 30000000000E-03
D ~r;;-l~l;lcHANGE
uuuLJ SIGN [PRINT[
SCI
•
2-6
Model 1155 Reference Manual
9/72
Keyboard Operations
ENTER
EXPONENT
Allows user to enter a number in scientific notation.
•
Enter6.02x10 23
GDG0
ENTER
EXPONENT
~
~
MANTI SSA
•
00Ip~~~TI
EXPONENT
6.02000000000E+23
L-------------
Enter 205 x 10 6
~IPRINTI
000 EXEpNo~E~T LJ
SCI
2.05000000000E+08
The 1155 converted the mantissa to 2.05000000000 and adjusted the exponent to
+08.
The following example illustrates the method for entering a negative exponent.
•
Enter 3.7 x 10
I.:lD~
L2J
· ~
-9
ENTER
EXPONENT
[Jc:Jlp~~~TI
~
~
MANTISSA
EXPONENT
3.70000000000E-09
The following shows how to enter a negative number, expressed in scientific
notation.
•
Enter -2 x 10 6
0
[PRINj
SCI
-2.00000000000E+06
2 x 1.0 6
-2
9/72
X
10 6
Model 1155 Reference Manual
2-7
Keyboard Operations
[W
ET
Sets the number of decimal places for printout. The number of decimal
places for printout can be set to any number from a to 9 inclusive.
Press SET DEC, then press the numeric key for the desired number of
places (0-9). The decimal place setting governs only the number of
places printed. It has nothing to do with the number of places carried
internally.
DEC
(
)
The following example shows the printout of the same number for various
decimal place settings.
KEYS
--------------------------------------------- PRINTOUT -----
1.23
1.235
1.23456
1.234560000
In each case, the printout is rounded to the number of decimal places
specified.
2-8
Model 1155 Reference Manual
9/72
Keyboard Operations
When entry of a number is terminated by pressing the PRINT or ENTER keys,
the number entered is printed in fixed point if possible. The maximum number
of positions for fixed point printout is fifteen. If a number requires more than
15 digits (including decimal places) it will automatically be printed in scientific
notation.
KEyS _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ PRINTOUT _ _ _ _ __
:L234567.00000
1234567.00000000
:L.23456700000E+06
I:"l
U
ENTER
EXPONENT
n
Q ~
~LJEJ
20 000 000 000
1~~~IDlpRINTI
2.00000000000E+:LO
IRESET IG!IJGJ
r--;l
ENTER 1.;:1 r;;I CHANGE IENTER I
~ EXPONENT ~~ SIGN
I ~~~ IDlpRlNTI
9/72
-20 000 000 000
-2.00000000000E+:LO
Model 1155 Reference Manual
2-9
Keyboard Operations
The PI key ( ) causes the contents of L to be transferred into U. The
previous contents of U are lost. The mathematical constant pi is
placed in the L register correct to 12 decimal places, as follows:
TI
= 3.~4~592653590
During printout the value of pi will be rounded to the number of decimal places
set for printout (0 through 9) or if printed in scientific notation, pi will be
printed as follows (printout set for two decimal places):
IRESETI U
~ IPRINTI
SCI
3.~4
3.14~59265359E+OO
LINE
SPACE
I
The LINE SPACE key causes one vertical line space on the printer.
If a mistake is made while entering a number, it can be erased by
CLEAR
ENTRY
pressing the CLEAR ENTRY key.
•
Enter 25
08 ~~~:~ [J[~]ENTERI
mistake
l-
25.00 ]
When the CLEAR ENTRY key is pressed, the print wheel s pins as a signal that
the 1155 has erased the previously entered number. The correctnumber may
then be entered .
•
Enter6xl0 22
n
ENTER J;I CLEAR ~ ENTER
2 i;lIENTERI
L:.J EXPONENT
~ ENTRY ~ EXPONENT ~~
1::1.
mistake
6.00000000000E+22
NOTE: If entry of a number has already been terminated by pressing the ENTER,
PRINT, PRINT SCI keys, then pressing CLEAR ENTRY has no effect. This is also
true if an arithmetic key or function key has been pressed.
2-10 . Model 1155 Reference Manual
9/72
Keyboard Operations
BINARY OPERATION KEYS
The operations +, -, x, -7-, and IA Ix are called binary operations because they
are performed on two numbers and produce a single result. The binary option
keys are:
These keys perform operations on numbers in Land U. The result is put in L
and U is cleared. These keys terminate number entry and cause the number that
was entered to be printed.
oD
and
0
also cause the result to be printed.
Adds the number in L to the number in U and stores the result in L.
Causes the previous entry to be printed along with a plus sign (in keyboard mode). U is cleared. To obtain the result, the PRINT key must
be pressed following the addition instruction. The first number in each
arithmetic operation may be terminated using the ENTER key.
KEYS _ _ _ _ _ _ _ _ _ _ _ _ _ _ L_ _ _ _U _ _ _ _ PRINTOUT _ __
75
75
9/72
75.00
37
75
112
o
112
o
37.00+
112.00
Model 1155 Reference Manual
2-11
Keyboard Operations
Subtracts the number in L from the number in U, stores the result in
L, and clears U to zero. In keyboard mode, the previous entry is
printed. To obtain the result, the PRINT key must be pressed following the subtraction instruction.
D
KEYS
L
00
25
I ENTER I
25
[:]
[J
I PRINT I
0
U
PRINTOUT
25.00
9
25
:16
0
9.00
16
0
:16.00
Multiplies the number in U by the number in L and stores the result in
L, then clears U to zero. Terminates a previous number entry (if any)
and prints the number. Prints the result automatically.
KEYS _ _ _ _ _ _ _ _ _ _ _L _ _ _ _ U _ _ _ PRINTOUT _ _ _ __
2.3
2.3
4.5
10.35
2-12
Model 1155 Reference Manual
2.30
2.3
o
4.50
:10.35
9/72
Keyboard Operations
Divides the number in U by the number in L. and puts the result into
L, then clears U to zero. Terminates a previous number entry and
causes the number to be printed. Prints the result (quotient)
automatically.
KEyS _ _ _ _ _ _ _ _ _ _ _ L _ _ _ _ U _ _ _ PRINTOUT _ _ __
37
37
4
9.25
37.00
37
a
4.00
9.25
Raises the absolute value of the number in U to the power of the
number in L. The result is put in Land U is cleared to zero. Terminates a number entry and causes the number to be printed. Prints the
result automatically.
KEYS
------------ L -----U ---- PRINTOUT -----2
2.00
2
9/72
5
2
32
o
5.00
32.00
Model 1155 Reference Manual
2-13
Keyboard Operations
Mixed Operations
The following examples illustrate sequential use of the binary keys.
EXAMPLE: 7 + 5 + 14 + 3 = 29
KEYS
L
7
7
ENTER
7
5
5
7
+
12
0
14
14
12
+
26
0
3
3
26
+
29
0
PRINT
29
0
U
PRINTOUT
7.00
5.00+
TAPE
7.00
5.00+
114.00+
3.00+
29.00
14.00+
3.00+
29.00
EXAMPLE: 12 - 18 + 33 - 4 = 23
KEYS
U
12
12
ENTER
12
118
18
12
-6
0
33
33
-6
+
27
0
4
4
27
23
0
23
0
PRINT
2-14
L
Model 1155 Reference Manual
PRINTOUT
112.00
18.00-
TAPE
112.00
118.0033.00+
4.0023.00
33.00+
4.0023.00
9/72
Keyboard Operations
EXAMPLE: 2 x 3 x 4 == 24
KEYS
L
2
2
ENTER
2
3
3
2
X
6
0
4
4
6
X
24
0
U
PRINTOUT
2.00
3.00
6.00
TAPE
2.00
3.00
6.00
4.00
24.00
4.00
24.00
3x4
EXAMPLE: S-=:2.4
KEYS
L
3
3
ENTER
3
4
4
3
X
12
0
5
5
12
2.4
9/72
U
0
--
PRINTOUT
TAPE
3.00
3.00
4.00
1.2.00
1.2.00
5.00
2.40
5.00
2.40
Model 1155 Reference Manual
2-15
Keyboard Operations
EXAMPLE: 2 x 3 + 4
=::
KEYS
L
U
2
2
ENTER
2
3
3
2
X
6
0
4
4
6
+
10
0
PRINT
10
0
EXAMPLE: 7 x 2 3
KEYS
-
4
=::
2
ENTER
2
PRINTOUT
TAPE
2.00
2.00
3.00
6.00
3.00
6.00
4.00+
:10.00
4.00+
:10.00
52
L
2
U
3
2
IAlx
8
0
7
7
8
X
56
0
4
4
56
52
0
52
0
Model 1155 Reference Manual
PRINTOUT
2.00
3
PRINT
2-16
10
3.00
8.00
7.00
56.00
TAPE
--
2.00
3.00
8.00
7.00
56.00
4.0052.00
4.0052.00
9/72
Keyboard Operations
EXAMPLE:
66 + 83 + 75
3
74.67
KEYS
L
66
66
ENTER
66
83
83
66
+
149
0
75
75
149
+
224
0
224
0
3
224
PRINT
3
74.666 ..
U
PRINTOUT
TAPE
66.00
*
83.00+
66.00
83.00+
75.00+
224.00
3.00
74.67
75.00+
224.00
3.00
74.67
0
FUNCTION KEYS
The function keys shown below are used to compute the indicated function of the
number in L and store the result in L. The number in U is not involved and is
not changed in any way.
The operations defined by these keys are called unary operations because they
are carried out on a single operant (number).
CHANGE
SIGN
0
0
I VfXT I
8
0
8
~ ~
G
G
G
G
*Carried to 13 significant digits internally.
9/72
Model 1155 Reference Manual
2-17
Keyboard Operations
The TO POLAR and TO RECT keys operate on the number in Land U and produce two results. The results are stored in Land U.
ITo!
ITo!
~
~
In keyboard mode, all function keys except CHANGE SIGN and ARC terminate
number entry and print the number. The result or results are printed
automatically.
CHANGE Changes the sign of the number in L from plus to minus or from minus
SIGN to plus. The sign of zero is not changed, however. It remains plus.
KEYS ____________________ L
U
5
5
-5
5
*
*
*
*
5
PRINT
CHANGE SIGN
CHANGE SIGN
PRINTOUT
5.00
5.00
5.00
~
Causes the number in L to be replaced by its reciprocal. The number
~ in the U register is unaffected. Overflow (Error 8) will occur if L is
equal to zero.
KEYS
4
l/X
U
.25
*
*
4
.2
.25
.25
.2
l/X
PROBLEM:
L
5
Given a and b compute
a~b
KEYS
L
U
RESET
Key in a
ENTER
Key in b
+
0
0
PRINTOUT
4.00
.25
.20
5.00
PRINTOUT
0
a
0
a
a
a
b
b+
0
a+b
l/X
0
l/(a+b)
l/(a+b)
*The CHANGE SIGN and l/X keys do not change the number in U. Remember, however,
that entry of a new number causes the number in L to be transferred to U.
2~18
Model 1155 Reference Manual
9/72
Keyboard Operations
O
X2
Causes the lUmber in L to be multiplied by itself (squared). The number
in U is unaffected. Overflow (Error 7) will occur if the absolute value
of the number in L is greater than or equal to 10 50 .
KEYS
RESET
5
X2
12
X2
L
U _ _ _ _ PRINTOUT _ _ _ __
0
5
25
0
0
0
12
144
25
25
5.00
25.00
12.00
144.00
~I Causes the number in L to be replaced by the square root of its absolute
~J value. The number in U is unaffected.
KEYS
RESET
25
/TXT
3
CHANGE SIGN
/fXi
L
U _ _ _ _PRINTOUT _ _ _ __
0
25
0
0
5
0
3
-3
25
25
1. 732 ...
25
PROBLEM: Given a and b compute
25.00
5.00
-3.00
1.73
/a 2 + b 2
KEYS
L
U _ _ _--.;PRINTOUT _ _ _ __
RESET
Key in a
0
a
0
0
X2
a2
0
a
a2
Key in b
b
a
X2
b2
a
b
b2.
+
a 2. + b 2
0
+
la2. +b 2
0
IfXf
9/72
la 2
+ b2
Model 1155 Reference Manual
2-19
Keyboard Operatiop-s
8
Causes the number in L to be replaced by its integer part. The number
in U is unaffected.
KEYS
L
U
8
8
0
0
5.99
5
8
8
13.01
13
2.9
-2.9
-2
5
5
13
13
13
8
INTGR
5.99
INTGR
113.011
INTGR
2.9
CHANGE SIGN
INTGR
PRINTOUT
8.00
8.00
5.99
5.00
113.011
13.00
-2.90
-2.00
Causes the number in L to be replaced by its absolute value and
rounded. L is then replaced by the factorial function*of the resultant
number. This operation does not affect the number of U. Overflow
(Error 1) will result if the absolute value of the original number in L
is greater than or equal to 69.5. A different error (Error 6) will occur
if the absolute value of the original number in L is greater than or
equal to 100.
KEYS
L
RESET
5
IXI !
4.5
0
5
120
0
0
4.5
-4.5
120
CHANGE SIGN
I X I!
-------- PRINTOUT ----------
0
4.49
24
4.49
I XI !
U
120
120
24
24
24
5.00
1120.00
4.49
24.00
-4.50
1120.00
*The factorial function is defined as follows.
xl =
{
1 if x = O.
1(2)(3) . . . (x) if x is a positive integer.
2 -20
Model 1155 Reference Manual
9/72
Keyboard Operations
Exponential and Logarithmic Functions
Two exponential function keys are available on the 1155.
The
I A Ix
key is described in the Binary Operations section.
The eX key is described below.
The number e is the base for natural or Napierian logarithms.
places:
e
O
=
To 12 decimal
2.7~8281828459
Causes the number in L to be replaced by eX where x is the original
number in L. U is not affected. Overflow (Error 7) will occur if the
number in L is greater than In 10 100 (approxImately 230.25851).
eX
KEYS
L
U _ _ _ _ PRINTOUT _ _ _ __
RESET
2
0
2
0
0
0
e
X
7.389 ...
1
-1
. 367 ...
1
CHANGE SIGN
eX
7.389 ...
7.389 ...
7.389 ...
2.00
7.39
-~.oo
.37
PROBLEM: Given x, compute e- x
KEYS
RESET
Key in
X
X2
CHANGE SIGN
e
9/72
X
e
2
L
U _ _ _.....;PRINTOUT _ _ _ __
0
x
0
0
x2
0
_X2
0
-x 2
0
Model 1155 Reference Manual
2-21
Keyboard Operations
Two types of logarithms are available on the 1155:
•
Base e logarithms using the I n Ix
I key.
log Ix Ikey.
•
Base 10 logarithms using the
~
In Ix I number in L and puts the result in L.
Computes the logarithm base e (natural log) of the absolute value of the
U is not affected. An attempt to
compute the logarithm of zero will cause an error condition (Error 3).
KEYS
L
0
2
.693 ...
RESET
2
lnlxl
10
CHANGE SIGN
lnlxl
10
-10
2.302 •••
U
------- PRINTOUT ----------
0
0
0
.693 .••
.693 •••
.693 •••
2.00
.69
-:LO.OO
2.30
GG!J
log Ix
I
Computes the logarithm base 10 (common log) of the absolute value of
the number in L and puts the result in L. U is not affected. An
attempt to compute the logarithm of zero will cause an error condition
(Error 3).
KEYS
RESET
2
loglxl
1000
CHANGE SIGN
loglxl
L
0
2
.301. ••
1000
-1000
3
RESET
loglxl
2 -22
Model 1155 Reference Manual
0
0
U _ _ _ _PRINTOUT ______
0
0
0
.301. ..
.301. ..
.301. ..
0
0
2.00
.30
-1000.00
3.00
ERROR 3
9/72
Keyboard Operations
Trigonometric Functions: SIN, COS, TAN
The following keys are used to compute the sine, cosine or tangent of a number.
BEJB
The sine, cosine and tangent functions may be computed for arguments
expressed in either degrees or radians.
•
Turns on the degrees light (above the DEG key) and specifies that the
trigonometric functions operate on arguments in degree measure. The
DEG key does not affect the numbers in the registers. When the 1155
is turned on it is set for degrees. The degree status remains in effect
until the RAD key is pressed.
•
Turns on the radians light (above the RAD key) and specifies that the
trigonometric functions operate on arguments in radian measure. The
RAD key does not affect the numbers in the registers. The radian
status remains in effect until the DEG key is pressed.
B
The relationships between degree measure and radian measure are shown below.
DEGREES = RADIANS X :L80
'IT
RADIANS
'IT
=
DEGREES X 180
Replaces the number in L by the sine of the number in L.
Replaces the number in L by the cosine of the number in L.
Replaces the number in L by the tangent of the number in L. If the
number in L is an odd multiple of 90 (DEG light on) or a multiple of
/2 (RAD light on) an error message will be printed (Error 2).
To compute sin x, cos x or tan x:
•
If not in keyboard mode, press RESET.
•
Set number of decimal places for printout.
•
Set 1155 to degrees or radians.
•
For each value of x,
key in x
... press SIN or COS or TAN.
9/72
Model 1155 Reference Manual
2-23
Keyboard Operations
For example, compute sin 60°, cos 45°, and tan 1000°,
KEYS
RESET
SET DEC 5
DEG
60
SIN
45
COS
:1000
L
U
0
0
0
600
SIN 600
0
0
0
0
0
45°
COS 45 0
SIN 60 0
SIN 60 0
COS 45 0
COS 45 0
1000
TAN
TAN 1000 0
PRINTOUT
60.00000
.86603
45.00000
.707.1.1
.1000.00000
-5.67:128
The secant (sec), cosecant (esc) and cotangent (cot) of a number are defined as
follows.
sec x
1
=-cos x
(cos x
f
0)
csc x
1
=-.smx
(sin x
f
0)
cot x
1
=-tan x
(tan x
f
0)
Sec x, csc x and cot x are computed using the COS, SIN. TAN and l/X keys,
as follows.
I COS II :1/X IComputes the secant of the number in L and puts the result in L.
U is not affected.
p utes the cosecant of the number in L and puts the result in L.
g~ 1:1/xlcom
U is not affected.
IT AN II.l/X Ico:uputes the cotangent of the number in L and puts the result in L.
U
IS
not affected.
NOTE: If the sine, cosine, or tangent is zero, then an error condition (Error 8) occurs
when the l/X key is pressed.
2 -24
Model 1155 Reference Manual
9/72
Keyboard Operations
EXAMPLE: Compute sec 30°
L
KEYS
RESET
SET DEC 5
DEG
30
COS
l/X
U
0
0
0
30
.86G03 ...
0
0
0
0
0
1.15470 ...
0
PRINTOUT
30.00000
.86603
1.15470 -(- SEC 30 0
Inverse Trigonometric Functions
The ARC key is used as a prefix to the SIN, COS and TAN keys to compute the
arcsine, arccosine and arctangent functions.
~ ~
Computes the arcsine of the number in L and puts the result in L. U is
~ ~not affected. The result will be in degrees if the DEG light is on or in
radians if the RAD light is on. If the absolute value of the original
number in L is greater than 1, an error condition (Error 4) occurs.
~
lr::lComputes the arccosine of the number in L and puts the result in L.
~ ~u is not affected. The result will be in degrees if the DEG light is on
or radians if the RAD light is on. If the absolute value of the original
number in L is greater than 1, an error condition (Error 4) occurs.
~ ~Computes
the arctangent of the number in L and puts the result in L.
~ ~u is not affected. The result will be in degrees if the DEG light is on
or in radians if the RAD light is on.
The 1155 computes the principal value of the arcsine, arccosine or arctangent,
as shown below.
9/72
DEG light on:
-90 0 < ARC SIN x < 90 0
0 0 < ARC COS x < 1800
-90 0 < ARC TAN x < 90 0
RAD light on:
-n/2 < ARC SIN x < n/2
o < ARC COS x < n
-n/2 < ARC TAN x < n/2
Model 1155 Reference Manual
2-25
Keyboard Operations
To compute arcsin x or arccos x or arctan x:
1.
If not in keyboard mode, press RESET.
2.
Set number of decimal places for printout.
3.
Set 1155 to degrees or radians.
4.
For each value of x:
a.
key in x
b.
press ARC, then sm
or ARC, then COS
or ARC, then TAN.
For example, compute arcsin .5, arccos (-.5) and arctan 1000 with results in
degrees.
KEYS
RESET
SET DEC 5
DEG*
L
U _ _ _ _ PRINTOUT _ _ _ __
0
0
.5
0
0
0
.5
ARC
SIN
30
0
.5
-.5
30
30
120
30
-.50000
:L20.0000
120
:LOOO.OOOOO
89.94270
.5
CHANGE SIGN
ARC
COS
0
0
.50000
30.00000
:LOOO
ARC
TAN
89.94270 ...
*To obtain the results in radians, press RAD instead of DEG.
2-26
Model 1155 Reference Manual
9/72
Keyboard Operations
In the following right triangle, a is the measure of angle BAC.
B
a
AL-----~------~C
. ex == a'
Sin
c '
cos ex == b
- •
c '
t an ex == -a
b
'"
.a
u. == arcsin c
co:
a
arccos b
- == arc t an 'I:"
c
u
Given a and c, compute ex in radians.
KEYS
L
U
RESET
SET DEC 5
RAD
0
0
0
Key in a
a
a
c
0
0
0
0
0
a
a/c
0
ENTER
Key in c
ARC
SIN
arcsin (al c)
-------- PRINTOUT ----------
a
c
a/c
0
arcsin (al c)
• 64350 .....~-- a
(radians)
For example, if a == 3 and c == 5:
3.00000
5.00000
.60000
9/72
Model 1155 Reference Manual
2-27
Keyboard Operations
Rectangular and Polar Coordinates
The following diagram and discussion show the relationship between rectangular
coordinates (x, y) and polar coordinates (r, e ).
y
y
I - - - - - - " AP
e
--------------¥~--~--~--~x
o
x
Conversion from rectangular to polar coordinates:
x
=
r cos
y = r sin
e
e
Conversion from polar to rectangular coordinates:
r
e=
where:
';x 2 +
=
tan
-180 < 9
-1T
2-28
_1
y2
Y
x
L
< 9 f::
180
(degrees)
1T
(radians)
Model 1155 Reference Manual
9/72
Keyboard Operations
ITOI
~
Converts polar coordinates (r, e ) where r is in U and e is in L to
rectangular coordinates (x, y). Stores the results in U and L with x in
U and y in L.
Before pressing TO RECT
After pressing TO RECT
e is given in degrees, the 1155 must be in DEG status before TO RECT is
pressed.
If
e is given in radians, the 1155 must be in RAD status before TO RECT is
pressed.
If
To convert from polar to rectangular coordinates:
1.
If not in keyboard mode, press RESET.
2.
Set number of decimal places for printout.
3.
Select degrees (DEG key) or radians (RAD key).
4.
For each set of values (r, e):
a.
Key in r, press ENTER.
b.
Key in
c.
Press TO RECT.
r
=
5,
8
e.
=
150 0
5.00000
150.00000
-4.33013 ~x
2.50000 ..-. y
9/72
r
=
2, 8
=
6 rad
2.00000
6.00000
1..92034 ....-x
-.55883 ....-y
Model 1155 Reference Manual
2-29
Keyboard Operations
/TO!
Converts rectangular coordinates (x, y) where x is in U and y is in L
to polar coordinates (r, 8 ). Stores the results in U and L with r in U
and 8 in L.
~
U
L
D
D
U
L
Before pressing TO POLAR
D
D
After pressing TO PO LAR
If the 1155 is in DEG status, 8 will be in degrees in the range:
e2
-180 <
180 0
If the 1155 is in RAD status, 8 will be in radians in the range:
-'IT
<
e
<
'IT
To convert from polar coordinates to rectangular coordinates:
1.
If not in keyboard mode, press RESET.
2.
Set number of decimal places for printout.
3.
Select degrees (DEG key) or radians (RAD key).
4.
For each set of values (x, y).
a.
Key in x, press ENTER.
b.
Key in y.
c.
Press TO POLAR.
x = 3,
y
= 4
3.00000
4.00000
5.00000 ...-r
53.:L30:L0 ...- 80
2-30
Model 1155 Reference Manual
x
=
3,
y
=
-4
3.00000
-4.00000
5.00000 ...-r
-.92730 ...- 8 rad
9/72
Keyboard Operations
MEMORY REGISTERS
The 1155 has 20 memory registers. Each memory register is identified by a
two digit number (00 through 19) called the address of the register.
00
0
05
0
10
0
15
0
01
9
06
0
11
0
16
0
02
4
07
0
12
0
17
0
03
0
08
-5
13
3.7
18
0
04
0
09
0
14
0
19
6.02E23
A memory register can store one number.
indicates that:
9
4
-5
3.7
6.02E23
is
is
is
is
is
stored
stored
stored
stored
stored
in
in
in
in
in
The above register diagram
register
register
register
register
register
01
02
08
13
19
All other registers contain O.
The following keys are used to manipulate numbers in memory registers.
KEY
ABBREVIA TION
CLEAR
ALL
REGS
CLR REGS
STORE
()
()
RECALL
()
()
ACCUM
STORE
()
9/72
STORE
RECALL
ACCSTORE
()
Model 1155 Reference Manual
2-31
Keyboard Operations
CLEAR
ALL
REGS
Clears all registers. Stores zeros in L, U and memory registers 00
through 19.
The CLR A LL REGS key has a lock to prevent accidental clearing of the
registers.
The STORE, RECALL and ACCSTORE keys must always be followed by a two
digit address designating the memory register involved in the operation.
Examples of legal operations are shown below
KEYS
----------------------- ABBREVIATION -------- COMMENTS
STORE
()
()
STORE
()
()
RECALL
()
()
ACCUM
STORE
()
()
GG
[J G
G []
DG
STORE 00
Store in register 00.
STORE .13
Store in register 13.
RECALL 0.1
Recall from register 01.
ACCSTORE .19
Accumulate store in
register 19.
The following examples are not correct memory operations.
KEYS _ _ _ _ _ _ _ _ _ _ _ _ REASON WHY NOT CORRECT _ _ _ __
STORE
()
()
RECALL
() () I
Must use two digit address.
There is no register 20. Addresses must
be whole number, 00 through 19.
-~
2-32
Model 1155 Reference Manual
9/72
Keyboard Operations
Stores the number in L in the memory register designated by the two
digit address following STORE. A STORE operation terminates a
number entry and causes the number to be printed. U is not affected.
STORE
l)
()
EXAMPLE: Key in 2.3 and store it in register 17. Then key in 9 and store in
register 05 and 06.
KEYS
L
U
RESET
0
2.3
2.3
0
0
0
9
9
9
2.3
2.3
2.3
2.3
STORE 17
9
STORE 05
STORE 06
05
06
17
2.3
9
9
9
2.3
2.3
PRINTOUT
2.30
STORE :17
9.00
STORE 05
STORE 06
The STORE operation put a copy of the number in L into the designated memory
register, replacing the previous content of the memory register. Note that the
operation does not change L.
RECALL
(1
()
Recalls the number in the indicated memory register to L. The previous content of L is transferred to U. A RECALL operation does not
change the content of the memory registers. In keyboard mode, the
number that is recalled is also printed.
The following example shows the contents of L, U and memory register 06
before and after a RECALL 06 operation.
9/72
L
U
REG 06
BEFORE
-5
7
2.3
AFTER
2.3
-5
2.3
Model 1155 Reference Manual
2-33
Keyboard Operations
The following example illustrates the use of STORE and RECALL.
EXAMPLE: 2 x 3 + 4 x 5
= 26
KEYS
L
U
RESET
0
2
2
3
6
0
0
0
2
0
6
4
4
5
20
0
6
6
4
0
6
6
6
6
6
6
26
26
20
0
0
6
6
6
2
ENTER
3
X
STORE OJ..
4
ENTER
5
X
RECALL OJ..
+
PRINT
ACCUM
STORE
( )
PRINTOUT
2.00
3.00
6.00
STORE OJ..
4.00
5.00
20.00
6.00
+
26.00
Adds the number in L to the number in the designated memory register
and stores the result in the memory register. Does not change the
number in L. U is unaffected.
( )
KEYS
RESET
CLR REGS
8
ACCSTORE OJ..
X2
ACCSTORE 02
5
ACCSTORE OJ..
X2
ACCSTORE 02
7
ACCSTORE OJ..
X2
ACCSTORE 02
RECALL OJ..
RECALL 02
2-34
01
L
U
00
01
0
0
8
8
64
64
5
5
25
25
7
7
49
49
20
138
0
0
0
0
0
0
64
64
64
64
25
25
25
25
49
20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
8
8
8
13
13
13
13
20
20
20
20
20
Model 1155 Reference Manual
02 •••
0
0
0
0
0
64
64
64
64
89
89
89
89
138
138
138
9/72
Keyboard Operations
If the operations are actually carried out, the printout should look like the
following.
.000000
8.000000
ACCSTORE OJ.
64.000000
ACCSTORE 02
5.000000
ACCSTORE 01
25.000000
ACCSTORE 02
7.000000
ACCSTORE 01
49.000000
ACCSTORE 02
20. OOOOOO~ LX
138. 000000 ~LX2
Exchange
If the RECALL key is pressed twice, without keying a register address, the
1155 exchanges the contents of Land U.
RECALL
RECALL
()
()
()
J
()
Exchanges the contents of Land U.
The following example shows the contents of Land U before and after pressing
RECALL RECALL.
u
L
t--_-_5_ _-I~ U
L
2.3
Before pressing RECALL RECALL
9/72
2.3
-5
After pressing RECALL RECALL
Model 1155 Reference Manual
2-35
Keyboard Operations
EXAMPLE: 3 - 4 x 5
KEYS
==
17
L
U
RESET
0
4
ENTER
4
4
0
0
0
5
5
4
X
20
0
3
3
3
20
20
20
3
3.00
20.00
-17
-17
0
0
-17.00
RECALL
RECALL
PRINT
PRINTOUT
4.00
5.00
20.00
The above problem can be done with fewer keystrokes as follows.
RESET, 4, ENTER
5, X
CHANGE SIGN
3, +
PRINT
2-36
Model 1155 Reference Manual
4.00
5.00
20.00
-20.00
3.00+
-:L7.00
9/72
3
PROGRAMMING
STORED PROGRAMS AND PROGRAMMING MODES
A stored program is a sequence of instructions stored in the program memory
of the 1155. An instruction is equivalent to one, two or three keystrokes. Up
to 511 keystrokes may be stored in the 1155's program memory.
There are five programming modes.
•
WRITE mode is used to store a program in the program memory.
•
LIST mode is used to list the stored program on the printer.
Instructions are listed as abbreviations.
•
RUN mode is used to run the stored program. In RUN mode the
1155 automatically performs the instructions stored in the program
memory.
•
INSERT mode is used to insert instructions into the stored program.
•
DELETE mode is used to delete instructions from the stored program.
The INSERT and DELETE modes are also called edit modes since they are used
in editing and debugging a program (see Section 4).
ABBREVIATIONS FOR INSTRUCTIONS DISCUSSED IN SECTION 2
KEYED IN AS
~
ACCUM
STORE
()
---------------- LISTED AS ------
-----------
A TO X
ACCSTORE :12
()
B
COMMENTS
Any memory register 00 19 may be used instead of
" 12" .
ARC
CHANGE
SIGN
OPP SIGN
CLEAR
ALL
REGS
CLR REGS
COS
9/72
Model 1155 Reference Manual
3-1
Programming
KEYED IN AS _ _ _ _ _ _ _ LISTED AS_ _ _ COMMENTS _ _ _ _ __
B
DEGREES
E TO X
a
ENTER
ENTER
EXPONENT
ENT EXP
FACTRL
INTEGER
log 10
In E
PI
8IPRrNTl
PRINT
PRINT SCI
~J
EJ
RADIANS
RECALL
()
()
RECALL
()
()
RECALL
RECALL
()
()
()
()
RECALL .10
Any memory register 00 - 19
may be used insteas of "10".
RECALL 99
Any integer greater than 19
causes L to be copied into U.
EXCG
Exchanges Land U.
RECIP
3-2
Model 1155 Reference Manual
9/72
Programming
KEYED IN AS _ _ _ _ _ _ _ LISTED AS _ _ _ COMMENTS _ _ _ __
I
~~~
(
)
I
o
SET DEC
SIN
LINE
SPACE
SPACE
SQ RT
STORE
()
o
()
TAN
TO POLAR
ITOI
TO RECT
~~J
o
8
D
o
8
8
o
D
Any memory register 00 19 may be used instead of
"18" .
ITOI
~
9/72
STORE 18
X SQ
+
x
o
ZERO
1
Any numeric 0 - 9.
Decimal point.
Model 1155 Reference Manual
3-3
Programming
In this section we will introduce these additional programmable instructions.
KEYED IN AS
ACCUM
STORE
()
()
-------------- LISTED AS -----COMMENTS
~
~
ACCSTORE N
~1sI1;l
~LJLJ
~.~
IF
NEG
Any program code 00 - 99
()
" 56" .
IF - GO TO N
()
56
RECALL
()
Any program code 00 - 99
may be used instead of
"56" .
IF - GO TO 56 may be used instead of
IF
NEG
()
GO TO 56
GO TO N
~~
()
_ _ _ _ __
()
~
~
Any program code may be
used.
RECALL N
STOP
STORE
()
()
~
~
STORE N
In addition, the following keys, located on the right side of the keyboard, are
used to write, list, run and edit programs.
RESET
START
ONE STEP
DELETE
WRITE
LIST
STORE IN CARD
INSER T
CLEAR PROG
LOAD FRO M CAR D
The above keys are called non-programmable keys since they may not be used
as instructions in a stored program.
3-4
Model 1155 Reference Manual
9/72
Programming
All other keys on the keyboard, except the CLEAR ENTRY key, may be used as
instructions in a stored program.
When the 1155 is running a stored program it behaves exactly as if the keys
stored in the program memory were being pressed one after the other in
keyboard mode, except:
•
No printing is done unless PRINT or PRINT SCI instructions are used
in the program.
•
An error of any kind causes the 1155 to return to keyboard mode.
this happens Land U are cleared.
If
SAMPLE PROGRAM
The following is a program to compute the value of
x
for a given value of x. The program is shown as it would appear when listed on
the printer in list mode.
++678 ....... . - - - - - - - checksum
program code--+--27
SPACE
STOP
PRINT
STORE 01
X SQ
1
instructions
RECALL 01
EXCG
PRINT
GO TO 27
In the above program, each instruction is equivalent to 1, 2, or 3 keystrokes.
Each instruction is listed as the abbreviation for the keystrokes it represents.
To use the above program:
WRITE the program in the 1155's program memory.
LIST the progranl and verify it.
RUN the program.
9/72
Mode1 1155 Reference Manual
3-5
Programming
WRITE MODE
Write mode is used to store a program in the program memory of the 1155.
CLEAR
PROG
-()I \
EJ
Clears program memory. Erases all program steps. The
CLEAR PROG key has a lock which prevents accidental
erasure of program memory.
Write mode is used to enter programs in the 1155's program
memory from the keyboard. To enter write mode from the
keyboard mode, press the WRITE key. This will cause the
light above the key to go on.
Up to 511 keys may be programmed into the 1155. However, if the key is not
programmable (except for RESET) the 1155 will ignore it. That is, it will not
be stored in the program memory.
Pressing RESET will cause the 1155 to return to keyboard mode and the light
above the WRITE key will go out.
If there is already a program in the program memory. WRITE will cause new
program steps to be appended to the program.
To Write a Program
NOTE:
3-6
1.
Press RESET
(to put the 1155 into keyboard mode)
2.
Press CLEAR PROG
(see note below)
3.
Press WRITE
(to put the 1155 into write mode)
4.
Key in the program.
CLEAR PROG is pressed only if it is desired to erase an already stored
program or set of programs. Omit this step if the intent is to append steps
to a program already stored.
Model 1155 RefexenceManual
9/72
Programming
Write the following program.
instructions, as follows.
Press, in order, the keys corresponding to the
KEYS
COMMENTS
PROG CODE 27
3 keys
------------------
LINE SPACE
STOP
PRINT
STORE 01
3 keys
X SQ
1
RECALL 01
3 keys
RECALL RECALL
2 keys
PRINT
GO TO 27
3 keys
The program is stored. Press RESET to terminate write mode and put the
1155 into keyboard mode.
LIST MODE
List mode is used to list (print out on the printer tape) the program in the
1155's program memory. The program may be listed in full or one step at a
time.
List mode is also used to compute and print a checksum of the stored program.
A checksum is a number which "represents" the program. It is used to verify
that a program has been correctly stored, either by hand or using the Model 511
Magnetic Card Reader.
9/72
Model 1155 Reference Manual
3-7
Programming
To enter list mode from keyboard mode, press the LIST key.
the key will come on indicating that the 1155 is in list mode.
The light above
\ /
-0I \
~
~
LI S T
Puts the 1155 in list mode. It is now ready to list
instructions beginning with the one at which it is now stopped.
8
+
Causes the 1155 to compute and print a checksum of the
program then stop at the first instruction in program
memory.
In list mode, causes the 1155 to start listing, beginning with
the step at which the machine is stopped and continuing
through the last instruction in program memory.
roNEl
In list mode, causes the 1155 to list one key step.
~
When listing one step at a time, instructions that are programmed by two
keystrokes (such as EXCG) will require two depressions on ONE STEP.
Instructions that are programmed by three keystrokes (for example, GO TO 23)
require three depressions of ONE STEP.
To list the instructions in program memory:
1.
Press RESET
2.
Press LIST, +
3.
Press START
(omit if already in keyboard mode)
(checksum is printed)
,Checksum
For example:
RESET, LIST +
START
++678
27
SPACE
STOP
PRINT
STORE 01
X SQ
.1
RECALL 01
EXCG
PRINT
GO TO 27
3-8
Model 1155 Reference Manual
9/72
Programming
The following shows the first few steps of the above program listed using ONE
STEP instead of START.
RESET, LIST +
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STE P
ONE STEP
++678
PROG CODE
2
7
SPACE
STOP
PRINT
STORE
o
.1.
Unused Program Steps
If ONE STEP is pressed immediately following a listing the 1155 prints the
number of unused program storage positions. The 1155 has 511 program
storage positions, each equivalent to one keystroke. The program below requires 20 positions. Therefore, there are 511 - 72 or 489 positions still
available. Instructions such as SPACE, PRINT and + require one position.
PROG CODE and GO TO instructions require three positions.
Press LIST,+,START
27
++678
SPACE
STOP
PRINT
STORE 0.1.
X SQ
.1.
RECALL 0.1.
EXCG
PRINT
GO TO 27
PRESS ONE STEP
Unused program space
9/72
~
N489
Model 1155 Reference Manual
3-9
Programming
RUN MODE
In run mode, the 1155 executes instructions previously stored in the program
memory. Run mode is entered from keyboard mode by pressing either the
STl\:ijT key or the ONE STEP key.
-0I \
If the 1155 is in keyboard mode, pressing START causes it to
start executing instructions stored in the program. The 1155 continues executing instructions until one of the following occurs:
8
•
If the 1155 encounters a STOP instruction it stops executing the
program and returns to keyboard mode. If START is pressed,
the 1155 will resume execution of the program, beginning with the
instruction following the STOP.
•
The operator may manually press STOP. The 1155 will complete
the instruction in progress, stop and return to keyboard mode.
Pressing START will cause the 1155 to resume program execution
from the point at which it was stopped.
•
If an error results from the execution of a stored instruction the
1155 prints an error message and returns to keyboard mode. If
this happens the Land U registers are cleared.
•
The user may press the RESET key while the program is running.
This will cause the 1155 to return to keyboard mode immediately
and clear Land U. Pressing START will not always restart the
1155 at the place at which it was interrupted.
After executing the last instruction in program memory, the 1155 will automatically "wrap around" to the first step in program memory and continue
execution.
Assume the following program has been entered into memory.
27
SPACE
STOP
PRINT
STORE 0.1
X SQ
.1
Computes
x
x
2 -
1
RECALL 0.1
EXCG
.PRINT
GO TO 27
3-10
Model 1155 Reference Manual
9/72
Programming
To RUN the program:
•
Press RESET
•
Press SET DEC 5
•
Press GO TO 27
•
Press START
(omit if already in keyboard mode)
(3 keystrokes)
The 1155 searches for PROG CODE 27, finds it and begins running the program.
It performs a SPACE then stops at the STOP instruction.
•
Key in x
=
2, press START.
The 1155 prints the value of x
and the value of x/(x 2 - 1)
•
Key in x
=
.66667
3, press START.
The 1155 prints the value of x
and the value of x/ (x 2 - 1)
•
2.00000
3.00000
.37500
Key in x = .7, press START
The 1155 prints the value of x
and the value of x/(x2 - 1)
.70000
-1.37255
This may be repeated for as many values of x as desired. When finished, press
RESET.
Halts automatic execution of a program and returns the 1155 to
keyboard mode. All normal keyqoard operations may be performed.
Automatic execution of the program may be continued by pressing
START.
The most common use of the STOP instruction is to stop execution of the program to permit entry of a number by the operator. After keying in the number,
the operator presses START and the 1155 resumes execution of the program.
9/72
Model 1155 Reference Manual
3-11
Programming
EXAMPLE: Given rand h, compute V
PROGRAM
=
'lTr2.h.
----------------------- COMMENTS ---------------------
23
SPACE
.,.------------.
p~i~~
Operator keys in r and presses START.
X SQ
S TO P ...,._------------PRI
NT
Operator keys in h and presses START.
X
'IT
X
PRINT
GO TO 23
PROGRAM CODE AND GO TO
A program code is a two digit number that marks a particular place in a program. There are 100 possible program codes, 00 through 99.
A GO TO instruction instructs the 1155 to search for a particular program code
and, on finding it, to begin executing instructions beginning with the instruction
immediately following the program code.
The following program has two program codes and one GO TO instruction.
program code - - - - - - - - - -..
• 110
SPACE
STOP
PRINT
STORE 011
program code
------------,!~
•
07
SPACE
STOP
PRINT
X SQ
RECALL 011
X
PRINT
GO TO instruction - - - - - - - - - - -..
• GO TO 07
In the above program, the program code 10 is used to mark the beginning of
the program. The program code 07 is referenced by the GO TO 07 instruction.
3-12
Model 1155 Reference Manual
9/72
Programming
PROG
CODE
()()
The PROGRAM CODE key is used to store a two digit program code
at a particular point in a program. Programming this operation
requires three keystrokes:
PROG CODE, digit, digit.
For example, the program code 10 is programmed as follows:
PROG
1~~i
IGOT.Oj
( )( )
n n
U
~
Causes the 1155 to search for a specific program code.
this operation requires three keystrokes:
GO TO, digit,
Programming
digit
For example, GO TO 07 is programmed as follows:
Im?18 []
In run mode, execution of the GO TO instruction causes program execution to
continue from the instruction immediately following the indicated program code.
In keyboard mode, a GO TO instruction causes the 1155 to find the indicated
program code, then return to keyboard mode. Automatic execution can then be
initiated by pressing the START key.
If the 1155 is instructed to search for a nonexistent program code, it will continue searching indefinitely. The search can be terminated by pressing the
RESET key.
It is customary to begin a program with a program code. Some programs may
have several "starting points," each one used for a different purpose. In this
case, a different program code is used for each starting point. It may also be
desired to store two or more programs in the 1155 at the same time. Each
program should begin with a different program code.
EXAMPLE: Assume that four programs are stored in the program memory of
the 1155. Program 1 begins at PROG CODE 10, Program 2 begins at PROG
CODE 20, Program 3 begins at PROG CODE 30 and Program 4 begins at PROG
CODE 40.
To Run Program 1 _ _ _ _ _ _ _ To Run Program 2 _ _ _ _ _ _ _ __
RESET
GO TO 10
START
9/72
RESET
GO TO 20
START
Model 1155 Reference Manual 3-13
Programming
To Run Program 3 _ _ _ _ _ _ _ To Run Program 4 _ _ _ _ _ _ __
RESET
GO TO 30
START
RESET
GO TO 40
START
A listing may begin at any program code. For example, suppose the following
program is stored in the 1155,
++200
.10
CLR REGS
SPACE
1.3
1.7
STOP
PRINT
ACCSTORE 01.
1.
ACCSTORE 02
GO TO 1.3
SPACE
RECALL 01.
PRINT
RECALL 02
PRINT
PRINT
STOP
GO TO 10
•
List the program, beginning at PROG CODE 17.
RESET .............- - - - - - - - (if not in keyboard mode)
GO TO 17
LIST
SPACE
START
RECALL 01.
PRINT
RECALL 02
PRINT
PRINT
STOP
GO TO 10
The listing begins with the SPACE instruction following PROG CODE 17 and
continues to the end of the program.
3-14
Model 1155 Reference Manual
9/72
Programming
If the content of L is negative (less than zero) a GO TO is executed
to the designated program code. If L is positive or zero, GO TO
IF
NEG
( )( )
is not executed but the program code is checked for validity, just
as if a GO TO instruction had been used. An IF - GO TO instruction is sometimes termed "conditional transfer."
The IF - GO TO instruction works as follows:
YES
::---II~
GO TO program code
execute next
step in the
program.
The IF - GO TO instruction may be used to:
1.
Terminate a loop
2.
Perform logic operations (conditional GO TO)
Terminating a Loop
EXAMPLE: Print the integers from 0 to 10, in descending order, then stop.
++921
PROGRAM:
10
~
J - s t o r e 10 in register 05
STORE 05
.------II~
20
RECALL 05
IF - GO TO
Put content of 05 in L
99----------------------------~
PRINT
Print L
:L
OPP SIGN
Subtract 1 from register 05
ACCSTORE 05J ~----------GO
L < 0
TO 20
99~------------------------------------------~
STOP
9/72
Model 1155 Reference Manual
3-15
Programming
The IF - GO TO instruction causes the program to jump to program code 99
when the content of register 05 becomes negative as a result of successive subtraction. The STOP instruction is then executed. If L is positive or zero, the
IF - GO TO 99 instruction is not executed, and the program continues to the
step following the IF - GO TO 99.
Condition GO TO
The IF - GO TO key may be used to program instructions of the form
IF
* GO TO
where the "*" may stand for a condition other than
GO TO or IF L» U GO TO).
II _ "
(for example, IF L
=
0
An IF * GO TO is called a conditional GO TO; where the "*" represents the condition under which the GO TO is executed. Conditional GO TO's are also called
branches.
The following flowchart symbol diagrams the operation of a conditional GO TO.
previous step
>-....................--'1.. program code
GO TO her!u true.
Continue here if false.
next step . . . - - . . /
Since many of the follOWing branching techniques change one or both of the
numbers to be compared, it is assumed that they will be stored in memory
registers when it is desired to save them.
3-16
Model 1155 Reference Manual
9/72
Programming
Examples of Conditional GO TO
Conditions comparing L to 0 (zero).
CONDITION _ _ _ _ _ _ _ _ _ _ STEPS TO PRODUCE BRANCR _ __
IF L < 0 GO TO prog code
IF - GO TO prog code
IF L > 0 GO TO prog code
CRG SIGN
IF - GO TO prog code
IF L =
o GO TO prog code*
,.
IF L
~
~
25
IF - GO TO prog code
CRG SIGN
IF - GO TO 25
GO TO prog code
(next step follows here)
25
IF - GO TO 25
GO TO prog code
(next step follows here)
0 GO TO prog code*
,.
IF L
25
IF - GO TO 25
CRG SIGN
IF - GO TO 25
GO TO prog code
(next step follows here)
o GO TO prog code*
,.
IF L lOGO TO prog code
IF - GO TO prog code
CRG SIGN
IF - GO TO prog code
Conditions comparing L to U.
IF L < U GO TO prog code
For example, U - L > 0
IF L > U GO TO prog code
For example, U - L < 0
- **
CRG SIGN
IF - GO TO prog code
IF - GO TO prog code
*Program code 25 may be replaced throughout by any other program code.
**The subtraction key subtracts L from U and places the result in L.
9/72
Mod~l
1155
:.a~ference
Manual
3-17
Programming
CONDITION _ _ _ _ _ _ _ _ _ _ STEPS TO PRODUCE BRANCH _ __
IF L = U GO TO prog code*
For example, U - L = 0
10
IF - GO TO 10
CHG SIGN
IF - GO TO 10
GO TO prog code
(next step follows here)
10
IF - GO TO 10
GO TO prog code
(next step follows here)
10
IF - GO TO prog code
CHG SIGN
IF - GO TO 10
GO TO prog code
(next step follows here)
IF L ~ U GO TO prog code*
For example, U - L;?: 0
IF L ~ U GO TO PROG code*
For example, U - L ~ 0
IF L I U GO TO prog code*
For example, U - L I 0
IF - GO TO prog code
CHG SIGN
IF - GO TO prog code
Looping
When a sequence of instructions is to be repeated, a loop may be used. A loop
is formed using GO TO (or IF - GO TO) followed by the program code that marks
the beginning of the key sequence to be repeated.
The following program illustrates the use of a loop.
10
SPACE
STOP
PRINT
X SQ
This is the loop. To terminate the
loop, press RESET.
PRINT
GO TO :LO
*Program code 10 may be replaced throughout by some other program code.
3-18
Model 1155 Reference Manual
9/72
Programming
Complex Loops
The following diagrams illustrate some of the more complex loops that can be
constructed using GO TO and IF - GO TO. Three dots in a vertical line stand
for a set of programmed instructions.
•
Two loops in one program:
10
•
•
MJ
TO 23J
•
GO TO
23
•
GO
•
Transfer to loop on condition:
12
•
•
•
r----IF -
I
I
I
I
I
GO TO 30
20
•
•
•
GO TO 12
L-30
•
~ThiS
..
is the main loop.
This is the conditional loop.
•
•
GO TO 20
9/72
Model 1155 Reference Manual
3-19
Programming
•
Loop within a loop:
08
•
20
•
r I
-
-
I
-I F - GO TO 30
GO TO 20-
L"'30
GO TO 08 - - - - - '
~
The INDIRECT key is used in two wasy:
~.
Following STORE, RECALL, and ACCSTORE, to use the content
of register 00 as a memory register.
After STORE, RECALL or ACCSTORE, the IND key replaces the address of a
memory register which normally follows these keys. When the 1155 encounters
an IND after any of these keys, while executing a program, it uses the number
in memory register 00 at that time for the address. When used as the address
of a register, the number in 00 must be a number between 1 and 19 inclusive.
•
Following GO TO and IF - GO TO, to use the content of register 00
as a program code.
After GO TO or IF - GO TO, the IND key replaces the program code which
normally follows these keys. When the 1155 encounters an IND after either of
these keys while executing a program, it uses the number in memory register
00 at that time for the program code. When used as a program code, the content
of 00 must be a number between 0 and 99 inclusive, and must refer to an actual
stored program code.
NOTES: If the content of 00 is not an integer, the 1155 will take that number
rounded to the nearest integer as the memory address or program code; the
number in 00 will not itself be changed by this operation.
In a program listing, the IND key appears as the letter N.
instruction GO TO, IND is listed as nGO TO N. n
3-20
Model 1155 Reference Manual
For example, the
9/72
Programming
STORE
()
§
Transfers the number in L to the memory register whose address
is the number in register 00, Does not change the number in L;
does not change the number in register 00.
~
(00)
The number in register 00 is used to address another memory
register, 01 through 19, The number in the register is transferred
to the L register. The number previously in L is moved to U: the
number previously in U is lost. The numbers in memory registers
00 through 19 are not changed.
~
Adds the number in L to the number in the memory register given
by register 00, The result is stored in the referenced memory
register. Registers L, U and 00 are not changed,
(00)
()
RECALL
()
()
ACCUM
STORE
( )
(00)
( )
KEYS
SET DEC 0
CLR REGS
9
STCf~E 00
:LO
STORE N
2
PRINT
RECALL N
PRINT
:L
ACCSTORE N
RECALL N
PRINT
[[TIJ [(;]
()
9/72
()
lOO)
L
U
00
09
PRINTOUT
0
09
09
10
10
2
2
0
0
0
09
09
10
10
0
0
09
09
09
09
09
0
0
0
0
10
10
10
2
10
10
2
2
09
09
10
10
10
1
1
11
11
10
10
1
1
09
09
09
09
10
11
11
11
11
Uses the content of register 00 as a program code; executes a GO
TO to the indicated program code, and continues running the
program from the instruction following that program code.
Model 1155 Reference Manual
3-21
Programming
EXAMPLES:
The following program illustrates the use of the GO TO N instruction.
COMMENTS _ _ _ _ _ _ _ _ __
PROGRAM
.10
SPACE
STOP
PRINT
STORE 00
GO TO r-:
Key in N. N can be 1, 2, 3, or 10.
Store N in register 00.
0.1 .~. . - - - - - - - - - - - - - - - .1
PRINT
GO TO .10
02 .•. . - - - - - - - - - - - - - - 2
2
PRINT
GO TO .10
03 . - - - - - - - - - - - - - - 3
3
3
PRINT
GO TO 10
...
If N = 1, execution continues from
program code 01 .
If N
= 2, execution continues from
program code 02.
If N = 3, execution continues from
program code 03.
Subroutine to compute
cosh x
=
x
-x
e +e
2
The value of x is assumed to be in U and the "return" program code in L. (See
SUBROUTINES).
PROGRAM _ _ _ _ _ _ _ _ _ _ COMMENTS _ _ _ _ _ _ _ _ _ __
90
STORE 00
Store the return address in 00
Exchange Land U; X is now in L.
EXCG
TO X
STORE 19
RECIP
RECALL 19
E
+
Compute eX and store result in 19.
Compute e- x .
Compute e x + e -x
2
-.
GO TO N
3-22
Model 1155 Reference Manual
Divide by 2
Go to the return address.
9/72
Programming
Subroutines
If the same (nearly the same) sequence of instructions is used in several
different places in a program, a programming technique called a subroutine
may be used to shorten the program and to clarify its function.
For convenience in discussion, the program exclusive of subroutines is termed
main program. GO TO instructions are used to reach ("call") the subroutine
from the main program, and program codes are used to mark the points where
the subroutine is to return to the main program.
To call a subroutine, use GO TO followed by the subroutine program code.
To return to the main program, store the program code marking the
return point in register 00, and use GO TO N at the end of the subroutine.
In addition to the call and return program codes. it is frequently desired to
store the values of variables to be manipulated by the subroutine, and recall
them during the execution of the subroutine. The result of the subroutine operation may also be stored for use later on by the main program.
Sample Subroutine
Below is a sample subroutine to calculate
cosh x
=
(e x + e -x) / 2
An instruction in the main program stores the value of x before calling the
subroutine and another instruction stores the subroutine result (the computed
value of cosh x) for use later in the main program.
9/72
Model 1155 Reference Manual
3-23
Programming
PROGRAM
COMMENTS
:LO
r
SPACE
STOP
PRINT
STORE 0:1
:1
:1
GO TO 90 1 :1.
90
Key in x
I
{Store x in 01
Enter return program
code in L. (Go to subroutine. )
{program code for
return from subroutine
MAIN
PROGRAM
•
•
STORE 00
RECALL 01
E TO X
STORE 19
RECIP
RECALL :19
+
2
Store return program
code. Recall x.
Compute cosh x
SUBROUTINE
..
STORE 02
GO TO N
3-24
Model 1155 Reference Manual
Store cosh x
Return to main program.
9/72
Programming
Below is another subroutine to compute cosh x, using another way to "pass"
the value of x to the subroutine.
PROGRAM _ _ _ _ _ _ _ _ _ _ COMMENTS _ _ _ _ _ _ _ _ _ __
•
•
:LO
STORE
STOP
PRINT
:L
:L
GO TO 90
:L:L
Key in x
Return program code.
Return program code
is now in L and x is in U.
MAIN
PROGRAM
•
90
STORE 00
EXCG
E TO X
STORE :L9
RECIP
RECALL :L9
Store return program
code in 00. Exchange
Land U: x is now in L.
SUBROUTINE
+
2
..
GO TO N
9/72
cosh x is now in L .
Return to main program.
Model 1155 Reference Manual
3-25
Programming
IF
NEG
( )( )
~
~
The IF - GO TO N instruction may be used to return from a subroutine which contains a loop; for example, an operation which is
to be performed a specified number of times before the return to
the main program is executed.
EXAMPLE:
In the following example, the desired number of iterations is
stored in Register 19; the return program code in in Register 00.
INSTRUCTIONS _ _ _ _ _ _ _ _ REMARKS _ _ _ _ _ _ _ _ _ __
25
Subroutine program code.
}
.l
OPP SIGN
ACCSTORE 19
EXCG
RECALL 19
}
IF - GO TO N
EXCG
•
}
•
GO TO 25
Decrease the loop counter by 1.
Save the content of U (if desired). If
the loop counter is negative, return
to main program. Save U register (if
desired).
Operation to be performed x times,
x
~
O.
MAGNETIC CARD READER
The Model 511 magnetic card reader provides permanent external storage of
programs written for the 1155.
To connect the card reader to the 1155 calculator:
1.
BE SURE THAT THE POWER SWITCH ON THE 1155 IS OFF.
2.
Connect the cord attached to the card reader to the socket in the rear
of the 1155. Make sure the two rows of prongs on the cord attachment
are aligned with the slots in the 1155; the shorter row of prongs should
be on top.
1.l55
REAR VIEW
- - -CONNECT
HERE
POWER CORD--/
3-26
Model 1155 Reference Manual
9/72
Programming
3.
Turn the 1155 power switch to ON. The card reader is now connected
and ready to operate.
Magnetic Cards
Cards used with the Model 511 are plastic, and are magnetically coated (sensitive) on one face only. Each card will store or read instructions in two directions
or "sides", labeled A and B. The card reader feeds the cards in one direction
only; the arrows printed on the sensitive face of the card show which way the
card should be inserted to read or store on the desired side (A or B).
~
w
SINGER
tSU51NE59 MACHIf'061!5
A
<t .....
V)
\ I
Either side will store the maximum number of keystrokes (511 or FEWER)
which the program memory can contain.
-Of
\
LOAD
FROM
CARD
Allows the user to enter instructions into the program memory from the
magnetic card reader.
To load a program from a card:
1.
Press RESET to reach keyboard mode.
2.
Press LOAD FROM CARD; the keylight will GO ON.
3.
Insert the card, printed face UP, into the slot in the front face of the
card reader. This activates the drive mechanism in the reader, and
the card feeds automatically.
Programs may be read in two directions or sides, labeled A and B; make sure
that the card is inserted in the correct direction for the program you wish to
load. When the reader has read the entire card (for example, one side), it stops
automatically; the card may then be removed.
\
/
The instructions on the card are appended to any instructions already in the
program memory. To erase any instructions from previous programs, press
CLEAR PROG before pressing LOAD FROM CARD.
-Of
STORE
IN
CARD
9/72
Allows the user to store instructions in the program memory onto a
magnetic card, using the magnetic card reader.
Model 1155 Reference Manual
3-27
Programming
To store a program on a card:
1.
Press RESET to reach keyboard mode.
2.
Press STORE IN CARD; the keylight will GO ON.
3.
Insert the card, printed face UP, into the slot in the front face of the
card reader. This activates the drive mechanism in the card reader,
and the card feeds automatically.
Programs may be stored on a card in two directions or sides, labeled A and B;
make sure that the card is inserted in the correct direction. Any instructions
already on the side of the card used for storing the program will be erased.
When the reader has fed the card entirely, storing all instructions in program
memory on one side of the card (A or B), it stops automatically. The card may
then be removed.
FRACTIONAL PART OF X
The fractional part of a number may be defined as:
y
=
FP(x)
=
x - INTEGER (x)
The following program computes and prints y after x is keyed in by the user.
PROGRAM
COMMENTS
:LO
CLR REGS
STOP
PRINT
RECALL 99
INTEGER
PRINT
STOP
J
J
key in x
Copy L into U
Compute and
print y.
CUBE ROOT
To compute the cube root of the number in L, use
3
RECI P
A TO X
3-28
Model 1155 Reference Manual
9/72
Programming
Va 2 + b 2
To compute c =
,
use
a
PRINT
b
PRINT
TO POLAR
EXCG
c is now in the L register.
SIGNUM FUNCTION
The signum function may be defined as:
y = SGN(x) = +1 if x > 0
Oifx= 0
-1 if x < 0
The following program computes and prints y after the user keys in x.
PROGRAM
--------------------
COMMENTS
.to
CLR REGS
STOP
PRINT
IF - GO TO 20
----------------------
Key in x
o
If x> 0, y = X O = 1
If x = 0, y = 0 0 = 0*
1
If x < 0, y = -1
TO X.
GO TO 30
A
20
OPP SIGN
30
PRINT
STOP
*The 1155 defines 00 = O.
9/72
Model 1155 Reference Manual
3-29
Programming
MODULUS FUNCTION
The modulus function may be defined in the following way:
r = p MOD q = P - q times INTEGER (p -;- q),
with the following restrictions:
p~O
q>O
O-::;r<q
Note that if p is not an integer, r will not be an integer. The quantity r is also
called "the remainder of p divided by q." The following program computes and
prints r after the user has keyed in p and q (in that order).
COMMENTS _ _ _ _ _ _ _ _ __
PROGRAM
:10
CLR REGS
STOP
PRINT
STORE 01
STOP
PRINT
STORE 02
INTGR
RECALL 02
Key in p and store it.
Key in q and store it.
Compute r and print it.
X
OPP SIGN
RECALL 0:1
+
PRINT
STOP
3-30
Model 1155 Reference Manual
9/72
4
EDITING A PROGRAM
INSERT MODE
-0-
IIN~~RT I
Puts the 1155 in insert mode. Instructions may be inserted into the
program. The light above the INSERT key will come on.
To Insert Instructions into a Stored Program
1.
List the program, one step at a time, until the place is reached where
instructions are to be inserted.
2.
Press RESET, then press INSERT.
3.
Insert the new instructions (key them in).
4.
Press RESET to terminate insert mode.
The above procedure will be applied to the following incorrectly stored program
which is missing three instructions.
INCORRECTLY STORED
PROGRAM
10
SPACE
STOP
STOP
PRINT
1
"
MISSING INSTRUCTIONS
~RINT
STORE 01
+
STORE 02
20
'J/72
RECALL 02
SPACE
PRINT "
A TO X
RECALL 01
X
PRINT
GO TO 20
STOP
Model 1155 Reference Manual
4-1
Editing a Program
The missing instructions are inserted as follows:
1.
List the program to the place where the first instruction is to be stored.
RESET, GO TO
2.
LIST
ONE STEP
ONE STEP
~O,
SPACE
STOP
Insert PRINT and STORE 01 instructions.
RESET, INSERT, PRINT, STORE
3.
O~
List the program to the next place where an instruction is to be inserted.
RESET, GO TO 20, LIST
ONE
ONE
ONE
ONE
4.
STEP
STEP
STEP
STEP
RECALL
o
2
SPACE
Insert STOP instruction.
RESET, INSERT, STOP
5.
Press RESET to return to keyboard mode.
The modified program should be listed and proofread to make certain that the
program is now correctly stored.
DELETE MODE
\ I
-0-
IDE'L~TE I
4-2
Puts the 1155 in delete mode and allows instructions to be deleted from
a program one keystroke at a time, while the program is being entered
or after it has been stored. DELETE is used with INSERT to edit
stored programs.
Model 1155 Reference Manual
9/72
Editing a Program
To Delete an Instruction During Entry
If an error is discovered while a program is being entered (for example, in
write mode):
1.
Press RESET to terminate write mode.
2.
Press DELETE to delete the last keystroke.
3.
Press START.
NOTE: If DELETE has been pressed in error (for example, the step is not to
be deleted), pressing RESET instead of START will return the 1155 to keyboard
mode without deleting any steps.
EXAMPLE:
The volume of a sphere. V
Program:
= 4/37fr 3
++492
10
SPACE
STOP
PRINT
3
A TO X
PI
X
4
X
3
PRINT
Enter the program:
RESET, CLEAR PROG, WRITE, PROG CODE, 1, 0,
SPACE, STOP, PRINT, 3, A TO X, 4
Lwrong key pressed
Delete the incorrect key:
RESET, DELETE, START
When DELETE is pressed, the light above it goes on; pressing START returns
the 1155 to keyboard mode, and the delete light goes out. The incorrect
instruction has been deleted. To continue storing the program, press:
WRITE, 7f, X, 4, X, 3, -;-, PRINT
9/72
Model 1155 Reference Manual
4-3
Editing a Program
To Delete Stored Instructions
1.
List the program, one step at a time, up to and including the step to be
deleted.
2.
Press RESET, DELETE, START for each keystroke to be deleted.
EXAMPLE: Suppose that the user, in storing a program to compute
x
x -1
2
loses his place and inadvertently keys in some instructions twice. Then the
listing of the program might be as follows:
++ 794 ~ checksum
27
SPACE
STOP
PRINT
STORE 01.
X SQ
STORE 01.
X SQ
}
Here are the duplicated steps.
1.
RECALL 01.
EXCG
PRINT
GO TO 27
To Delete the Duplicated Steps:
KEYS
---------------------- PRINTOUT
RESET, LIST, +,
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
4-4
Model 1155 Reference Manual
++794
PROG CODE
2
7
SPACE
STOP
PR INT
STOR~}
X SQ
duplicated
steps
9/72
Editing a Program
There are four keystrokes to be deleted, as follows:
RESET
DELETE,
DE LE TE,
DELETE,
DELETE,
START
START
START
START
(deletes
(deletes
(deletes
(deletes
X SQ)
1)
0)
STORE)
NOTE: The DELETE key works backward from the last key reached by LIST,
ONE STEP.
Now, LIST the program:
RESET, LIST, +, START
++678
27
note altered checksum
SPACE
STOP
PRINT
STORE 01
duplicated keystrokes deleted
X SQ
1
RECALL 01
EXCG
PRINT
GO TO 27
To Edit Stored Programs
1.
List the program in full.
2.
Note errors: steps to be deleted and inserted.
3.
Press RESET.
4.
List the program one step at a time until the first error is reached. Use
GO TO to begin the LIST, ONE STEP at a program code other than the
beginning of the program.
5.
DELETE and/or INSERT steps as desired.
EXAMPLE: Compute the mean of a set of scores, x.
M
9/72
=
(Lx.)
1
IN ,
where N· is the number of scores.
Model 1155 Reference Manual
4-5
Editing a Program
CORRECT PROGRAM:
++200
.10
CLR REGS
SPACE
13
STOP
PRINT
ACCSTORE 01
.1
ACCSTORE 02
GO TO .13
.17
SPACE
RECALL 01
PRINT
RECALL 02
PRINT
...
PRINT
STOP
GO TO .10
Suppose, however, that several incorrect steps had been inadvertently stored,
so that the listing is as follows:
10
.13
....- - incorrect step
17
~--
4-6
Model 1155 Reference Manual
step omitted
9/72
Editing a Program
To edit the program:
KEYS
-------------------------------PRINTOUT
RESET, GO TO 13, LIST
ONE STEP
ONE STEP
ONE STEP
ONE STEP
ONE STEP
RESET, DELETE, START
DELETE, START
INSERT, 0, 1
RESET, GO TO 17, LIST
ONE STEP
ONE STE P
ONE STEP
ONE STEP
RESET,
INSERT, PRINT
STOP
PRINT
ACCSTORE
1
o
(DELETE 01
(DELETE 11
(INSERT 0, 11
SPACE
RECALL
o
1
(INSERT PRINT)
Now, list the edited program:
RESET, LIST, +, START
CHECKSUMS
A number called the checksum is used to identify each program. To obtain the
checksum in a program listing, press
RESET, LIST, +,
The checksum will be printed, preceded by the symbols "++". Modifying the
program usually changes the checksum. It is possible, but unlikely, that two
different programs will have the same checksum.
The checksum is used to verify that a program has been correctly loaded, either
by hand or using the Model 511 Magnetic Card Reader. If the checksums of the
original program listing and of the program loaded are not the same; it is not
the same program or the card has been loaded or stored incorrectly.
If the checksums of the original program listing and the program just loaded do
not match follow the procedure below.
1.
9/72
List the first few steps of the program using LIST, ONE STEP, to see if
they match the original program. Be sure to list several steps since many
programs begin in similar ways.
Model 1155 Reference Manual
4-7
Editing a Program
2.
If the program has been loaded from a card, check to see that the cable
connecting the 1155 to the card reader is attached properly, reload the
card, and print the checksum.
3.
Using the GO TO key, jump to a few program codes selected at random and
list the program in their vicinity as an additional check on the identify of
the loaded program.
4.
List the entire program and check it against the original listing. If the
program was loaded manually from the keyboard look for missing or extra
steps as well as incorrect ones.
5.
If the listings match, run the program as a test for malfunctions. If the
program runs properly, the original checksum may be in error.
4-8
Model 1155 Reference Manual
9/72
APPENDIX A - FUNCTION KEYS
SUMMARY
KEYS
U
L
D
D
- - - ERROR
CODES
u + L
0
ERROR 7 IF lu + L/ > 10 100
u - L
0
ERROR 7 IF
u X L
0
ERROR 7 IF lu X LI > 10 100
..
0
ERROR 5 IF L = 0
UL
0
ERROR 1 IF lULl> 10 100
0
L2
U
ERROR 7 IF ILl > 10 50
I/TXT I
vTLT
u
l/L
U
D
D
u
~
G
8
Integer
part of
- L/ > 10 100
ERROR 8 IF L = 0
U
L
[GJ*
0
L
Iu
ILI !
eL
~
log
e
ILl
U
ERROR 7 IF L
ERROR 6 IF L
?: 69.5
?: 100
U
ERROR 1 IF L
?: 231
U
ERROR 3 IF L = 0
*The number in L is rounded before I X I! is computed.
9/72
Model 1155 Reference Manual
A-I
Appendix A. Function Keys
KEYS
U
ERROR CODES
loglO L
U
ERROR 3 IF L = 0
L
U
L
U
SIN L
U
COS L
U
TAN L
U
ERROR 2 IF L IS ODD
MULTIPLE OF 90°
SIN- l L
U
ERROR 4 IF ILl> l
COS- l L
U
ERROR 4 IF ILl > ~
TAN- l L
U
L
8
~
0
0
B
0
B EJ
B ET
ET
B
POLAR
~
QtJ
RECT
TAN-~ (U/U
U COS L
VL 2 + U2 ERROR
~o
IF U = L = 0
U SIN L
*The inverse functions compute the principal values:
_90°::; sin -1 L ::; 90°
0°< cos -1 L::; 180°
_90°::; tan -1 L ::; 90°
A-2
Model 1155 Reference Manual
9/72
APPENDIX B - MISCELLANEOUS PROCEDURES
LOADING PAPER TAPE
f
'
.
. ~.:Io"
,.,
-
l".',."''' ~
-.
,~
The paper tape roll is contained under the hinged cover loc ated on top of the
calculator. To replace the paper tape, raise the hinged cover a nd proceed as
follows:
9/ 72
1.
Remove the rem a ining roll by lifting the roll from the well a nd tearing
the tape to free the spool.
2.
Depress PAPER ADVANCE until the remaining paper is free.
3.
T ear lea ding edge of new roll to form a smooth , flat edge .
4.
Drop the roll in the well , leading edge faCing down.
Model 1155 Reference Manual
B-1
Miscellaneous Procedures
5.
Depress PAPER ADVANCE key until paper appears above the paper
tear off.
6.
After closing the cover, the machine is ready to operate.
CHANGING INK ROLLER
The 1155 conta ins a unique ink roller tha t eliminates ribbons. Designed for
maxim um convenience, each ink roll er las ts much longer than a ribbon, and
eliminates ribbon threading a nd stained h ands.
Simply replace the old ink cartridge with a new one according to the following
procedure. The new cartridge is conveniently packaged in a plastic container
so you never have to touch the ink.
B-2
Model 1155 Reference Manual
9/72
Miscellaneous Procedures
9/72
1.
Remove the snap-on plate on the front of the machine.
2.
Push Locking Tab (yellow) to left and hold.
3.
Grasp ink cartridge with right hand and extract.
4.
Release Locking Tab (yellow).
new ink cartridge.
5.
Hold Locking Tab (yellow) to left. Grasp new ink cartridge by ends.
Insert new cartridge, checking to see that both ends of the inker shaft
are inserted in the yokes.
6.
Release Locking Tab (yellow).
place.
7.
Replace the snap-on front plate.
Calculator is now ready to receive
Make sure ink cartridge is locked in
Model 1155 Reference Manual
B-3
INDEX
A
E
Absolute value
abbreviation of
ACCSTORE
ACCUM STORE key
IND
Addition key
listed as
Address of a register
ARC key
listed as
Arccosine
Arcsine
Arctangent
2-13,2-19,2-20
3-1
3-1,3-4,3-14
2-34,3-1,3-4
3-4,3-20,3-21
2-11
3-3
2-31
2-17,2-25
3-1
2-25,2-26,2-27
2-25,2-26,2-27
2-25,2-26,2-27
B
Binary operation keys
2-11
examples of mixed operations
2-14,2-15,2-16
Branches
3-16,3-17,3-18
Editing a program
stored programs
modes
ENTER key
listed as
ENTER EXP key
listed as
Error 2
Error 3
Error 4
Error 6
Error 7
Error 8
Error messages
Exponent
negative
Exponential function key,
base e
listed as
4-5
4-5
1-2,3-1
2-1
3-2
2-1,2-7
3-2
2-23
2-22
2-25
2-20
2-19,2-21
2-18,2-24
1-4
2-1,2-5
2-5
Factorial function key
listed as
Flowchart symbol
Fixed point notation
Fractional part of x
Function keys
2-17,2-20
3-2
3-16
2-6
3-28
2-17
2-17,2-21
3-2
F
C
Card reader control mode(s)
1-2
CHANGE SIGN key 2-1,2-4,2-17,2-18
scientific notation
2-5
listed as
3-1
Checksum
4-7
CLEAR ALL REGS key
2-32
3-1
listed as
CLEAR ENTRY key
2-1,2-10,3-5
CLEAR PROG key
3-4,3-6
Conditional GO TO
3-16
Cosecant
2-24
COS key
2-17,2-23
listed as
3-1
Cotangent
2-24
Cube root
3-28
D
DEG key
listed as
Degrees
DELETE key
duplicated steps
mode
stored instructions
Division key
listed as
9/72
2-23,2-25
3-2
2-23
3-4,4-2
4-4
1-2,4-2
4-4
2-13
3-3
G
GO TO key
3-4,3-13
conditional
3-21,3-22,3-23,3-24,3-25
IND
3-4,3-20
I
IF NEG key
listed as
IND
IND key
Input/ output
INSERT key
mode
Instructions
INTGR key
listed as
3-4,3-15
3-4
3-4,3-20,3-26
3-20,3-21
2-1
3-4,4-1,4-2
1-2,3-1,4-1
3-1
2-17,2-20
3-2
Model 1155 Reference Manual
1-1
Index
Polar coordinates
2-28,2-29
conversion to rectangular
2-28,2-29,2-30
TO POLAR key
2-30
PRINT key
2-1
listed as
3-2
PRINT SCI key
2-1,2-6
listed as
3-2
Printer
1-1
Program code(s)
1-4,3-12
Program memory
1-3
Program storage positions
3-9
Programming modes
1-2,3-1
K
2-1
1-2,2-1
2-1
Keyboard
Keyboard mode
keys
L
LINE SPACE key
2-1,2-10
listed as
3-3
LIST
1-2,3-4,3-9,3-14
LOAD FROM CARD
3-4,3-27
Logarithm base 10 key
2-17,2-22
listed as
3-2
Logarithm base e key 2-17,2-21,2-22
listed as
3-2
2-21
Logarithmic functions
Loops
3-18,3-19,3-20
complex
3-19
terminating
3-15
R
Radians
2-23
RAD key
2-23
listed as
3-2
RECALL key
2-33,2-35,2-36,3-2
exchange
2-35
listed as
3-2
IND
3-4
Reciprocal key
2-17,2-18
listed as
3-2
Rectangular coordinates
2-28
conversion to polar
2-28,2-30
TO RECT key
2-29
Registers
1-3,2-2,2-31
Working
1-3,2-2
memory
1-3,2-31
RESET key
2-1,3-4
RUN mode
1-2,3-1,3-10,3-11
M
Magnetic card reader
cards
LOAD FROM CARD
STORE IN CARD
Main program
Mantissa
Memory register
address of
Modes
Modulus function
Multiplication key
listed as
3-26
3-27
3-27
3-27,3-28
3-23
2-5
1-3,2-31
2-31
1-2,3-1
3-30
2-12
3-3
S
N
Non-programmable keys
3-4
0
ONE STEP key
ON-OFF switch
3-4,3-8,3-9,4-7
1-5
P
Pi key
listed as
1-2
Model 1155 Reference Manual
2-10
3-2
Scientific notation
Secant
SET DEC key
listed as
Signum function
SIN key
listed as
START key
STOP key
STORE key
IND
listed as
STORE IN CARD
2-6,2-7
2-24
2-1,2-8
3-3
3-29
2-17,2-23,2-24
3-3
3-4,3-8,3-9,3-10
3-4,3-11
2-31,2-32,2-33
3-4
3-3
3-4,3-27,3-28
9/72
Index
Stored programs
Square root key
listed as
Squaring a number
listed as
Subroutines
examples
main program
Subtraction key
listed as
3-1
2-17,2-19
3-3
2-19
3-3
3-23
3-23
3-23
2-4
3-3
TAN key
listed as
TO POLAR key
listed as
TO RECT key
listed as
Trigonometric functions:
SIN, COS, TAN
inverse
2-17,2-23
3-3
2-30
3-3
2-29
3-3
T
2-23
2-25
U
Unary operations
Unary operation keys
1-3
2-17
W
Working register
Lower
Upper
WRITE key
mode
9/72
1-3
1-3,2-2
1-3,2-2
3-4,3-5,3-6
1-2,3-1,3-6
Model 1155 Reference Manual
1-3
FRIDEN MODEL 1155 ADVANCED PROGRAMMABLE CALCULATOR
REFERENCE MANUAL
Publication No. 55-538
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