Java Glossary : two's complement arithmetic
Last updated 2004-06-28 by Roedy
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Glossary : T words : two's complement arithmetic.
- two's complement arithmetic
- Java internally uses (or emulates) two's complement arithmetic. Positive
numbers are stored in binary. That means that for example the number 13 would
be written 0x0d = 00001101 = 1*8 + 1*4 + 0*2 + 1*1. The high order bit is called
the sign bit. For signed quantities such as byte, short int and long, when that
high order bit is a 1, we consider the number negative. To represent a negative
number we first invert each bit, then add 1. We would write -13 this way: 0x0d -
> 00001101 -> 11110010 -> 11110011 -> 0xf3. Whenever you do any
operation on a byte, it is first sign extended to an int. So so 13 -> 0x0d ->
00001101 -> 00000000000000000000000000001101 -> 0x0000000d and -13 ->
0xf3 -> 11110010 -> 11111111111111111111111111110010 -> 0xfffffff3.
When you do arithmetic the results can be too big to represent. The arithmetic
is done modulo 2 to the 32nd power, which is a fancy way of saying the high
order bits of the result are discarded. The overflow may turn on the high order
bit, making the result look negative. Don't confuse two's complement
with two's compliment an activity you do in the back seat of a car
in an attempt to talk someone out of their clothes.
