ones' complements

Noun

ones' complement (plural ones' complements)

1. The number obtained by subtracting a given n-digit binary number from 2ⁿ-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. 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 0 to -(2ⁿ⁻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.

   Synonyms:

   logical complement