binarywidth

Binary width, or bit width, is the number of binary digits (bits) required to represent a value in binary, or the number of parallel binary signals in a data path. In computing, it usually refers to the width of a fixed-size integer type or a data bus.

Formally, for a nonnegative integer n > 0, the binary width is floor(log2(n)) + 1. For n = 0, width is zero in strict mathematical terms, though some conventions treat it as one to reflect representation in certain contexts. In practical terms, fixed-width integer representations use a defined width that determines how many bits are available for values and operations.

In fixed-width representations, common widths are 8, 16, 32, and 64 bits. The width determines the representable range: for unsigned values, 0 to 2^w - 1; for signed values in two's complement, -2^(w-1) to 2^(w-1) - 1. The width also governs arithmetic behavior, such as wraparound on overflow and the alignment of registers, memory, and instructions.

Bit width is applied to data paths and storage media, where the width of a bus or register defines how many bits can be moved or stored in parallel. It influences performance, power consumption, and compatibility across system components.

Practical use of binary width includes memory allocation, type checking, and ensuring values fit a given format, as well as designing algorithms and encodings that depend on bit-length, such as compression and cryptography. Related terms include bit length, word size, and bus width.