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Difference between revisions of "gate universality"

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'''Gate universality''' is a concept that refers to individual [[logic gates]], primarily [[NAND]] and [[NOR]], being [[functionally complete]]. Converting complex logic functions into [[NAND logic|NAND]] and [[NOR logic|NOR]]-based logic can sometimes allow additional optimizations by removing redundant sets of [[pMOS transistor|pMOS]] and [[nMOS transistor|nMOS]] pairs of [[transistor]]s.
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'''Gate universality''' is a concept that refers to individual [[logic gates]], primarily [[NAND]] and [[NOR]], being [[functionally complete]].
  
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In [[CMOS]], converting complex logic functions into [[NAND logic|NAND]] and [[NOR logic|NOR]]-based logic can sometimes allow additional optimizations by removing redundant sets of [[pMOS transistor|pMOS]] and [[nMOS transistor|nMOS]] pairs of [[transistor]]s.
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{| class="wikitable"
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! [[logic gate|Gate]] !! [[Boolean function]] !! [[NAND logic]] !! [[NOR logic]]
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|-
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| [[not gate|NOT]] || <math>Q = \bar{A}</math> || <math>Q = \overline{AA}</math>  || <math>Q = \overline{A+A}</math>
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|-
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| [[and gate|AND]] || <math>Q = AB</math> || <math>Q = \overline{AB}</math>  || <math>Q = \overline{A+B}</math>
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|-
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| [[or gate|OR]]  || <math>Q = A+B</math> || <math>Q = \overline{\bar{A}\bar{B}}</math>  || <math>Q = \overline{\bar{A}+\bar{B}}</math>
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|}
  
 
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Revision as of 00:59, 23 November 2015

Gate universality is a concept that refers to individual logic gates, primarily NAND and NOR, being functionally complete.

In CMOS, converting complex logic functions into NAND and NOR-based logic can sometimes allow additional optimizations by removing redundant sets of pMOS and nMOS pairs of transistors.

Gate Boolean function NAND logic NOR logic
NOT Equation upper Q equals upper A overbar Equation upper Q equals ModifyingAbove upper A upper A With bar Equation upper Q equals ModifyingAbove upper A plus upper A With bar
AND Equation upper Q equals upper A upper B Equation upper Q equals ModifyingAbove upper A upper B With bar Equation upper Q equals ModifyingAbove upper A plus upper B With bar
OR Equation upper Q equals upper A plus upper B Equation upper Q equals ModifyingAbove upper A overbar upper B overbar With bar Equation upper Q equals ModifyingAbove upper A overbar plus upper B overbar With bar
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