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, popcount, sideways sum, or bit summation

Examples of applications of the Hamming weight include

• In modular exponentiation by squaring, the number of modular multiplications required for an exponent e is log2 e + weight(e). This is the reason that the public key value e used in RSA is typically chosen to be a number of low Hamming weight.
• The Hamming weight determines path lengths between nodes in Chord distributed hash tables.
• IrisCode lookups in biometric databases are typically implemented by calculating the Hamming distance to each stored record.
• In computer chess programs using a bitboard representation, the Hamming weight of a bitboard gives the number of pieces of a given type remaining in the game, or the number of squares of the board controlled by one player’s pieces, and is therefore an important contributing term to the value of a position.
• Hamming weight can be used to efficiently compute find first set using the identity ffs(x) = pop(x ^ (x-1)). This is useful on platforms such as SPARC that have hardware Hamming weight instructions but no hardware find first set instruction.
• The Hamming weight operation can be interpreted as a conversion from the unary numeral system to binary numbers.
• In implementation of some succinct data structures like bit vectors and wavelet trees.

Implementation

// Swift Default function
func hammingWeight(_ n: Int) -> Int {
	return n.nonzeroBitCount
}

// Math logic
func hammingWeight(_ n: Int) -> Int {
	var sum = 0 
	var n = n
	while n != 0 {
		sum += 1
		n &= (n-1)
	}
	return sum
}

Reference

• https://en.wikipedia.org/wiki/Hamming_weight