Universal Logic Gates - Technical Articles - All About Circuits

NAND and NOR gates are widely known to be universal logic gates, meaning that any other logic gate be made from NAND or NOR gates. This article discusses other ... 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Introduction Auniversallogicgateisalogicgatethatcanbeusedtoconstructallotherlogicgates. TherearemanyarticlesabouthowNANDandNORareuniversalgates,butmanyofthesearticlesomitothergatesthatarealsouniversalgates.Thisarticlecoverstwoinputlogicgates,demonstratesthattheNANDgateisauniversalgate,anddemonstrateshowothergatesareuniversalgatesthatcanbeusedtoconstructanylogicgate. TwoInputLogicGates For2logicalinputs,thereare16possiblelogicgates.Table1definesthe16logicgates,showslogicalsymbol,behaviorinsymboliclogic,providesname,notes. Peoplearemostfamiliarwiththeonesthatarenamed:NAND,NOR,AND,OR,XOR.Table1includesthese,aswellasANDandORgateswitheitherinputnegated,logic0andlogic1(whicharen'treallylogicgates),andsomegatesthataren'treallybinary.   OutputwhenABis         Gate# 00 01 10 11 SymbolicLogicalDescription Symbol Name/Description Note 0 0 0 0 0 0 Alwayszero Notreallyagate 1 0 0 0 1 A&B AND   2 0 0 1 0 A&~B AandNotB Universal 3 0 0 1 1 A A NotBInary 4 0 1 0 0 ~A&B BandNotA Universal 5 0 1 0 1 B B NotBinary 6 0 1 1 0 (A&~B)|(~A&B) XOR AlsoNotEqualsFunction 7 0 1 1 1 A|B OR 8 1 0 0 0 ~(A|B) NOR Universal 9 1 0 0 1 (A&B)|(~A&~B) XNOR AlsoEqualsFunction 10 1 0 1 0 ~B NotB NotBinary 11 1 0 1 1 A|~B AorNotB Universal 12 1 1 0 0 ~A NotA NotBinary 13 1 1 0 1 ~A|B BorNotA Unversal 14 1 1 1 0 ~(A&B) NAND Universal 15 1 1 1 1 1 Always1 Notreallyagate Table1:2InputLogicGates NANDGateisaUniversalGate NANDgatescanbeconnectedtoformanyotherlogicgates.Figures1,2,3showhowNANDgatescanbeconnectedtoformINVERTER,AND,andORgates.Thesegatescanbecombinedtoformtheotherlogicgatesaccordingtothesymboliclogicdefinitionsintable1. Figure1:ConnectingaNANDgatetomakeanINVERTERgate Figure2:ConnectingNANDgatestomakeanANDgate Figure3:ConnectingNANDgatestomakeanORgate OtherUniversalGates Gates2,4,11,and13areuniversalgates.Toprovethis,wedemonstratebuildingNANDgateswiththesegates.Gates7and8arethesamegatebutwithdifferentinputsinverted.Gates9and10arethesamegatebutwithdifferentinputsinverted.Provingthatgates2and11areuniversalisenoughtoprovethatgate4and13areuniversalaswell. Gate11:A|~B Figures4and5showshowgate11canbecombinedtocreateINVERTERandANDgates.INVERTERandANDgatescanbeconnectedinseriestoconstructaNANDgate.Becausegate11canbeusedtoconstructaNANDgate,andaNANDgateisauniversalgate,gate11isauniversalgate.Sincegates11and13aremirrorsofeachother,gate13isalsoauniversalgate. Figure4:Connectinggate11(A|~B)tocreateanINVERTERgate. Figure5:Connectinggate11(A|~B)tocreateanANDgate.Theremaybeawaytodothiswithfewergates.Thefigurehereistheonetheauthorcouldderivethequickest. Gate2:A&~B Figures6and7showshowgate2canbecombinedtocreateINVERTERandANDgates.INVERTERandANDgatescanbeconnectedinseriestoconstructaNANDgate.Becausegate2canbeusedtoconstructaNANDgate,andaNANDgateisauniversalgate,gate2isauniversalgate.Sincegates2and4aremirrorsofeachother,gate4isalsoauniversalgate. Figure6:Connectinggate2(A&~B)tocreateanINVERTERgate. Figure7:Connectinggate2(A&~B)tocreateanANDgate. Conclusion Thisarticlehasdiscussedlogicgates,universalgates,demonstratedthattheNANDgateisauniversalgate,andproventhatfouradditionaluniversallogicgatesexist.Thisisaninterestingacademicexercise.Inpractice,theauthorwouldrecommendstickingtousingNANDgatesasuniversalgatesbecausetheyaresocheapandsmalltoconstruct,orifdoingboardleveldesignusingchipswiththeactualgatesthatarewantedandnotusinguniversalgates. RelatedContent CombinationalLogicCircuitDesignandSimulationUsingGates GateDriverSolutionsforFastSwitchingApplications ResearchersSeekOut“FastestEverLogicGates”ViaLasers HalfBridgeandGateDriveMeasurementsandTechniques What’sNewwithLogicGates? LearnMoreAbout: booleanlogic digitallogic digital Comments 3Comments Logintocomment I ilane November13,2015 lovedthenixietubespic! Like. Reply C Chanducsr July21,2017 It’sgoodifweremembertheuniversalgates.But,ifwedon’trememberwhattheyareexactlythenitisnotallgoingtobeeasytorealized. Isthereanytrickthathelpsustoknowwhetherthegivengateisauniversalgate?!!?? Like. Reply M MIS42N August25,2018 Twothingstoremember:[1]oneconnection(eitherinputoroutput)mustinvert(turna0intoa1,ora1intoa0).[2]thegate(ignoringtheinversion)iseitheranORoranANDgate. Like. 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