Two's complement

A binary encoding for signed integers in which a negative value is represented by inverting the bits of its positive magnitude and adding one. Its fixed-width arithmetic naturally wraps modulo a power of two.

Bitwise NOT: A unary operation that flips every bit in a binary value. Flipping every bit is the complement step used to form a negative value.
Binary numeral system: A positional numeral system that represents values using the digits zero and one. Two's complement assigns signed meaning to ordinary binary bit strings.
Sign-magnitude: A signed-number encoding that stores a sign bit separately from the bits representing magnitude. Unlike two's complement, it has both positive and negative zero and needs separate arithmetic handling.
Integer representation: A scheme for encoding whole numbers as finite sequences of bits. Two's complement is the dominant fixed-width representation for signed machine integers.
John von Neumann: A mathematician and computer pioneer who contributed to the design of stored-program computers. His 1945 computer design report described binary arithmetic using a complement representation.
Modular arithmetic: Arithmetic in which values wrap around after reaching a fixed modulus. Fixed-width two's-complement addition behaves as arithmetic modulo the word size's power of two.
Unsigned integer: An integer representation in which every bit contributes to a nonnegative magnitude. The same bit pattern has a different value when interpreted as signed rather than unsigned.
One's complement: A signed binary encoding that forms negative values by inverting every bit of the positive value. It omits the add-one step and therefore has two representations of zero.
Arithmetic logic unit: A processor component that performs integer arithmetic and logical operations. The same binary adder handles signed two's-complement addition without a separate sign path.
EDVAC: An early stored-program computer designed in the 1940s and completed in 1951. Its design history helped establish complement arithmetic in electronic computers.

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