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Editing boolean algebra/majority function
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{| class="wikitable" style="float: right; text-align: center;" | {| class="wikitable" style="float: right; text-align: center;" | ||
! colspan="4" | 3-input Majority | ! colspan="4" | 3-input Majority | ||
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− | + | A 3-input majority function can be implemented using the following Boolean function <math>\text{MAJ}(x,y,z) = (x \land y) \oplus (x \land z) \oplus (y \land z)</math>. | |
− | A 3-input majority function | ||
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− | == | + | == Properties == |
− | The majority function is a [[unate function]], symmetric, monotone increasing, and self-dual. It therefore, with the addition of | + | The majority function is a [[unate function]], symmetric, monotone increasing, and self-dual. It therefore, with the addition of an [[inverter]] it can satisfy all the conditions needed to be [[functionally complete]] (i.e. '''{'''[[not gate|NOT]], MAJ'''}''' is a complete set). Being self-dual means that <math>\text{MAJ}(\bar a, \bar b, \bar c) = \overline{\text{MAJ}(a, b, c)}</math> which could yields various hardware implementation optimization - such as floating the [[inversion bubble|inversion point]] to a more efficient location. |
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== Majority gate == | == Majority gate == |