ones' complement

ones' complement (plural ones' complements)

1. (computing) The number obtained by subtracting a given n-digit binary number from ${\displaystyle 2^{n}-1}$ (which yields the same result as the logical complement).

   The ones' complement of 0xAAAA is 0x5555 on a 16-bit machine, and 0xFFFF5555 on a 32-bit machine.

2. (computing) The convention by which bit patterns with high bit 0 represent positive numbers from 0 to ${\displaystyle 2^{n-1}-1}$ directly, while bit patterns with high bit 1 represent negative numbers from 0 to ${\displaystyle -(2^{n-1}-1)}$, n being the word size of the machine, and the numeric complement of a number is its ones' complement.

   Computers that use ones' complement arithmetic have two representations for zero, all 0's and all 1's.

• logical complement

• complement
• diminished radix complement
• two's complement