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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, or the digit sum of the binary representation of a given number and the ℓ₁ norm of a bit vector. In this binary case, it is also called the population count,[1] popcount, sideways sum,[2] or bit summation.[3]
| String | Hamming weight |
|---|---|
| 11101 | 4 |
| 11101000 | 4 |
| 00000000 | 0 |
| 678012340567 | 10 |
| ||
| A plot for the population count (Hamming weight for binary numbers) for (decimal) numbers 0 to 256.[4][5][6] |
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