Bitweight

Bitweight is a measure in computer science and digital electronics that counts the number of one bits in a binary representation of a value. It is also known as the Hamming weight or population count. For a non-negative integer n, the bitweight equals the count of 1s in its binary form; for example, 13 is 1101 in binary, so its bitweight is 3. For a bitvector or bitstring, the bitweight is the sum of its bits.

The concept is distinct from bit length, which counts the total number of bits regardless of value. Bitweight reflects sparsity or density of a bit pattern and is widely used in algorithms, data structures, and digital signal processing. In cryptography and coding theory, the bitweight of keys, error vectors, or codewords relates to certain properties such as strength or error-detecting capabilities; in statistics and information theory, it indicates sparsity of representations.

Computing bitweight can be done by simple iteration, or more efficiently with algorithms such as Brian Kernighan’s method (repeatedly clearing the lowest set bit) or by using processor-specific instructions (popcount on x86 and ARM architectures) and SIMD. For large data sets, bitweight is often computed over sizeable bitarrays or bitmasks by summing the weights of machine words.

Bitweight appears in discussions of hash functions, Bloom filters, and syndrome calculations, where knowing the number of active bits can affect performance or probability estimates. The term is sometimes used interchangeably with Hamming weight, population count, or bit count.

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