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two's complement

The way every modern processor stores signed integers - the top bit counts as a large negative amount, and one adder works for both signs.

In n-bit two's complement, bit n-1 has weight -2^(n-1) and the others their usual positive weights, giving the range -2^(n-1) to 2^(n-1)-1; -x is (NOT x) + 1, which equals 2^n - x modulo 2^n.

Examples

  • In 8 bits, −5 is 11111011 (0xFB): invert 00000101 to 11111010, then add 1.

See also

negation signed integer sign bit
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