Editing Hamming weight (section)

{{Short description|Number of nonzero symbols in a string}}
{{redirect|popcnt|The CPU instruction|SSE4#POPCNT_and_LZCNT}}
{{Use dmy dates|date=May 2019|cs1-dates=y}}
The '''Hamming weight''' of a [[string (computer science)|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 given set of [[bit]]s, this is the number of bits set to 1, or the [[digit sum]] of the [[Binary numeral system|binary representation]] of a given number and the [[Taxicab geometry|''ℓ''₁ norm]] of a bit vector. In this binary case, it is also called the '''population count''',<ref name="Warren_2013"/> '''popcount''', '''sideways sum''',<ref name="Knuth_2009"/> or '''bit summation'''.<ref name="HP-16C_1982"/>
 
{|class="wikitable" align="right"
|+Examples
!String
!Hamming weight
|-
|'''111'''0'''1'''
|4
|-
|'''111'''0'''1'''000
|4
|-
|00000000
|0
|-
|'''678'''0'''1234'''0'''567'''
|10
|}

[[File:Hamming weight plot.png|thumb|right|A plot of Hamming weight for numbers 0 to 256.<ref name="formulae">{{cite web |url=https://formulae.org/?script=examples/Population_count |title=Population count the Fōrmulæ programming language |first=Laurence |last = R.Ugalde |website=Fōrmulæ |access-date=June 2, 2024}}</ref>]]