Ones' complement

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The ones' complement of a binary number is the value obtained by inverting (flipping) all the bits in the number (that is, changing each 1 to a 0 and each 0 to a 1). The name "ones' complement" refers to the fact that such an inverted value, if added to the original, would always produce an "all ones" number (the term "complement" refers to such pairs of mutually additive inverse numbers, here in respect to a non-0 base number). This mathematical operation is primarily of interest in computer science, where it has varying effects depending on how a specific computer represents numbers. A ones' complement system or ones' complement arithmetic is a system in which negative numbers are represented by the inverse of the binary representations of their corresponding positive numbers. In such a system, a number is negated (converted from positive to negative or vice versa) by computing its ones' complement. An N-bit ones' complement numeral system can represent integers in the range −(2N−1−1...

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