Integer Types Bits and bytes • A bit is a single two-valued quantity: yes or no, true or false, on or off, high or low, good or bad • One bit can distinguish between two cases: T, F • Two bits can distinguish between four cases: TT, TF, FT, FF • Three bits can distinguish between eight cases: TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF • In general, n bits can distinguish between 2n cases • A byte is 8 bits, therefore 28 = 256 cases Number systems • The binary (base 2) number system uses two “binary digits, ” (abbreviation: bits) -- 0 and 1 • The octal (base 8) number system uses eight digits: 0, 1, 2, 3, 4, 5, 6, 7 • The decimal (base 10) number system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 • The hexadecimal, or “hex” (base 16) number system uses sixteen digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F Everything is a number? • Everything in the computer is stored as a pattern of bits – Binary distinctions are easy for hardware to work with • Numbers are stored as a pattern of bits – Computers use the binary number system • Characters are stored as a pattern of bits – One byte (8 bits) can represent one of 256 characters • So, is everything in the computer stored as a number? – No it isn’t, it’s stored as a bit pattern – There are many ways to interpret a bit pattern Counting • To count up in any number system, – add 1 to the rightmost digit – if the result is higher than the largest digit, • set that digit to zero and carry to the next place • repeat addition of 1 and carrying as many times as necessary • Example: In hex, 4A6FF + 1 = 4A700 Computers use binary numbers • People like to use decimal numbers • Computers use binary numbers – Java translates decimal numbers into binary – The computer does all its arithmetic in binary – Java translates binary results back into decimal • You occasionally have to use numbers in other number systems Using octal and hex numbers • Computers use binary, but the numbers are too long and confusing for people--it’s easy to lose your place • Octal or hex is better for people • Translation between binary and octal or hex is easy – One octal digit equals three binary digits 101101011100101000001011 5 5 3 4 5 0 1 3 – One hexadecimal digit equals four binary digits 101101011100101000001011 B 5 C A 0 B Writing octal and hex integers • Integers are usually written in decimal notation: 7, 532, 28 • To write a number in octal, just start with a zero: 02, 0657, -077 – but don’t use the digits 8 or 9 ! • To write a number in hexadecimal, start with 0x or 0X: 0xA, 0X43AB5, -0xFFFF – the “digits” A through F can be upper or lower case Integer types • There are four integer types – byte – occupies one byte (surprise!) • can hold numbers in range –128 to 127 – short – occupies two bytes • can hold numbers in range –32768 to 32767 – int – occupies four bytes • can hold numbers up to + or – 2 billion – long – occupies eight bytes • can hold numbers up to about 19 digits • literals are written with a L suffix: 123456789L Floating-point literals • Floating-point literals are written with a decimal point: 8.5 -7.923 5.000 • Floating-point numbers may also be written in “scientific notation”– times a power of 10 • We use E to represent “times 10 to the” • Example: 4.32E5 means 4.32 x 105 • float literals are written with a F suffix – Examples: 8.5F -7.923F 5.000F 4.32E5F – If you don’t have the F suffix, type double is assumed Floating point types • There are two floating-point types – float – occupies four bytes • Can hold numbers in the range 3.4E38 to 1.4E-45 • Accuracy is about nine digits – double – occupies eight bytes • Can hold numbers in the range 1.7E308 to 4.9E-324 • Accuracy is seventeen or eighteen digits Number “width” • Numeric types are considered wider or narrower than other numeric types – This is based partly on number of bytes occupied – Also based on how large a number it can hold • Java doesn’t mind if you assign a narrow value to a wide variable: int n = 3; • Java is not happy if you assign a wide value to a narrow variable: byte b = 7139946; Widening and narrowing • You can always assign a narrower value to a wider variable byte short int long float double – This is called widening • You can do something special to assign a wide variable to a narrower variable – This is called narrowing Casts • You can convert (cast) one numeric type to another • When you widen, no explicit cast is necessary – But it doesn’t hurt • When you narrow, an explicit cast is required – This requirement is made to help avoid errors • Casting tells Java that the value in the wider type will fit in the narrower type • Java checks to make sure that the cast works, and gives you an error if it didn’t Example casts short s = 0; int i = 0; double d = 0.0; d = i; // legal d = s; // legal i = s; //legal i = d; // illegal s = d; // illegal s = i; // illegal i = (int) d; // legal s = (short) d; // legal s = (short) i; // legal d = 3.7E20; i = 50000; // The following give // runtime errors: s = (short) i; i = (int) d; The End

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