# two’s complement arithmetic : Java Glossary

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 - ⇒ 0000110111110010111100110xf3. Whenever you do any operation on a byte, it is first sign extended to an int. So so 130x0d00001101000000000000000000000000000011010x0000000d and -130xf311110010111111111111111111111111111100100xfffffff3. When you do arithmetic the results can be too big to represent. The arithmetic is done modulo 2 to the 32 nd 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.