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The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a string of bits, this is the number of 1's in the string. In this binary case, it is also called the population count, popcount, or sideways sum. It is the digit sum of the binary representation of a given number and the norm of a bit vector.The Hamming weight is named after Richard Hamming although he did not originate the notion. Irving S. Reed introduced a concept, equivalent to Hamming weight in the binary case, in 1954.Hamming weight is used in several disciplines including information theory, coding theory, and cryptography. Examples of applications of the Hamming weight include:The population count of a bitstring is often needed in cryptography and other applications. The Hamming distance of two words A and B can be calculated as the Hamming weight of A xor B.