two's complement

1. The number obtained by complementing every bit of a given number and adding one. A number and its complement add to 2ⁿ, where n is the word size of the machine.

   The two's complement of 0xAAAA is 0x5556 on a 16-bit machine, and 0xFFFF5556 on a 32-bit machine.

2. The convention by which bit patterns with high bit 0 represent positive numbers from 0 to 2ⁿ⁻¹-1 directly, while bit patterns with high bit 1 represent negative numbers from −1 to -2ⁿ⁻¹, n being the word size of the machine, and the numeric complement of a number is its two's complement.

   Nearly all modern computers use two's complement for integer arithmetic.

regular