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.
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“When Socrates, after being relieved of his irons, felt the relish of the itching that their weight had caused in his legs, he rejoiced to consider the close alliance between pain and pleasure.”
—Michel de Montaigne (1533–1592)