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boolean algebra/majority function
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Majority function (sometimes quorum function) is a threshold function that produces a 1 if and only if the majority of the inputs are 1. Otherwise, the output is 0. This function is only defined for three or more odd inputs. The majority function can be found in various applications such as adders, subtractors, hash functions, and Muller C-element.

Equation MAJ left-parenthesis x 1 comma x 2 comma period period period comma x Subscript n Baseline right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 1 comma 2nd Column if sigma-summation Underscript i equals 1 Overscript n Endscripts x Subscript i Baseline greater-than-or-equal-to StartFraction n Over 2 EndFraction 2nd Row 1st Column 0 comma 2nd Column otherwise period EndLayout

A 3-input majority function can be implemented using the following Boolean function Equation MAJ left-parenthesis x comma y comma z right-parenthesis equals left-parenthesis x logical-and y right-parenthesis circled-plus left-parenthesis x logical-and z right-parenthesis circled-plus left-parenthesis y logical-and z right-parenthesis .

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