Xor And Xnor Gate Truth Table & Symbol - Electrical4U

XOR Gate Truth Table ... The above truth table's binary operation is known as exclusive OR operation. It is represented as A ⊕ B. The symbol of ... SkiptocontentMenuOctober11,2020February24,2012byElectrical4UContentsWhatisanXORGate?XORGateTruthTableXORGateCircuitDiagramLogicalSymbolofXORGateMultipleInputXORGate3InputXORGateWhatisanXNORGate?XNORGateTruthTableXNORGateCircuitDiagram3InputXNORGateApplicationsofXORGatesWhatisanXORGate?AnXORgate(alsoknownasanEOR,orEXORgate)–pronouncedasExclusiveORgate–isadigitallogicgatethatgivesatrue(i.e.aHIGHor1)outputwhenthenumberoftrueinputsisodd.AnXORgateimplementsanexclusiveOR,i.e.,atrueoutputresultoccursifone–andonlyone–ofthegate’sinputsistrue.Ifbothinputsarefalse(i.e.LOWor0)orbothinputsaretrue,theoutputisfalse.XORrepresentstheinequalityfunction,i.e.theoutputistrueiftheinputsarenotalike;otherwise,theoutputisfalse.AcommonwaytoremembertheXORis“musthaveoneortheother,butnotboth”.AnotherwaytolookatanXORgate:amodulosumoftwovariablesinabinarysystemlookslikethis:ThelogicgateperformsthismodulosumoperationwithoutincludingcarryisknownasXORgate.AnXORgateisnormallytwoinputslogicgatewheretheoutputisonlylogical1whenonlyoneinputislogical1.Whenbothinputsareequal,eitherare1orbothare0,theoutputwillbelogical0.ThisisthereasonanXORgateisalsocalledananti-coincidencegateorinequalitydetector.ThisgateiscalledXORorexclusiveORgatebecauseitsoutputisonly1whenitsinputisexclusively1.Indigitalelectronics,otherlogicgatesincludeNOTgates,ORgates,NANDgates,andNORGates.XORGateTruthTableTruthtableslisttheoutputofaparticulardigitallogiccircuitforallthepossiblecombinationsofitsinputs.ThetruthtableofanXORgateisgivenbelow:Theabovetruthtable’sbinaryoperationisknownasexclusiveORoperation.ItisrepresentedasA⊕B.ThesymbolofexclusiveORoperationisrepresentedbyaplusringsurroundedbyacircle⊕.XORGateCircuitDiagramTheaboveexpression,A⊕Bcanbesimplifiedas,Letusprovetheaboveexpression.Infirstcaseconsider,A=0andB=0.Insecondcaseconsider,A=0andB=1.Inthirdcaseconsider,A=1andB=0.Infourthcaseconsider,A=1andB=1.SoitisprovedthattheBooleanexpressionforA⊕BisAB̅+ĀB,asthisBooleanexpressionsatisfiedalloutputstateswithrespecttoanXORgate’sinputsconditions.FromthisBooleanexpression,onecaneasilyrealizethelogicalcircuitofanXORgate,andthiswillbeasshown,LogicalSymbolofXORGateAnXORgateislogicallyrepresentedas,MultipleInputXORGateAlthoughXORgatescanonlyhavetwoinputs,youcanperformtheXORoperationusinganynumberofinputs(e.g.3inputXORoperationor4inputXORoperation).MorethantwoinputsXORoperationisthat,whentheoddnumberofinputsinthegatearea1,theoutputis1,andwhennoneoreventhenumberofinputsis1,theoutputislogical0.3InputXORGateLetusrealizeanXORgatewiththreeinputsA,B,andC.Now,asperthedefinitionofXORoperationwithmorethanthreeinputs,thetruthtablewouldbe,Thistruthtablecanbeelaboratedas,Fromtheabove-elaboratedtruthtable,itisfoundthattheXORoperationofthreebinaryvariablesisequivalentto,XORoperationofonevariablewiththeresultofXORoperationsoftheothertwovariables.Fromtheabovetruthtable,WhatisanXNORGate?TheXNORgate(alsoknownasaXORN’T,ENOR,EXNORorNXOR)–andpronouncedasExclusiveNOR–isadigitallogicgatewhosefunctionisthelogicalcomplementoftheexclusiveORgate(XORgate).Logically,anXNORgateisaNOTgatefollowedbyanXORgate.TheXORoperationofinputsAandBisA⊕B;therefore,XNORoperationthoseinputswillbe(A+B)̅.ThatmeanstheoutputoftheXORgateisinvertedintheXNORgate.IntheXORgateoperation,theoutputisonly1whenonlyoneinputis1.Theoutputislogical0whenbothinputsarethesame,meaningtheyareeither1or0.ButintheXNORgate,theinverseistrue.Hencetheoutputis0whenonlyoneinputis0,andtheoutputis1whenbothinputsarethesame(i.e.eithertwo0’sortwo1’s).SeetheXNORgatetruthtablebelowforavisualrepresentationofthis.XNORGateTruthTableThetruthtableoftheXNORgateisshownbelow:ThelogicalXNORoperationisrepresentedby⊙.Thatisadotsurroundedbyacircle.TheexpressionofXNORoperationbetweenvariablesAandBisrepresentedasA⊙B.Nowagain,thetruthtableissatisfiedbytheequationAB+ĀB̅.Hence,itisprovedthatA⊙B=AB+ĀB̅.ThesamecanbeprovedbyusingK-mapalso.XNORGateCircuitDiagramTheexpressionofXNORoperationcanberealizedbyusingtwoNOTgates,twoANDgates,andoneORgateasfollowers,ThesymboloftheXNORgate:3InputXNORGateLiketheXORgate,anXNORgateonlyexistswithtwoinputs,butforXNORoperationwithmorethantwoinputs,wehavetousemorethanoneXNORgates.XNORoperationwithmorethantwoinputsislikethat.Whenthereareoddnumbersofinputsinhighorlogical1condition,theoutputwillbe0;otherwise,theoutputwillbe1.Now,Fromthiselaboratetruthtable,thelogicalsymbolofthreeinputsXNORgatecanberepresentedas,ApplicationsofXORGatesThemainapplicationoftheExclusiveORgateisintheoperationofhalfandfulladder.Ifwelookatthetruthtablecarefully,wewillfindthatthefirstthreeresultsaretotallysatisfyingtheprocessofbinaryaddition.Still,inthelastinputsequencei.e.whenboththeinputsare1,theresultaccordingtotheruleofadditionshouldbe0withacarry1.Inthetruthtable,wearegettingthedesired0butamissing1.Tosolvethisproblemwhiledesigninganadder’scircuit,anANDgateisaddedtotheEx-ORgateinparallel.Wewillshowthecircuitoftheadderindetail.Fromtheabovediagram,wecanseethatthetwoinputsaregoingthroughanExclusive-ORgateandanANDgateparallellyinthehalfaddercircuit.Andwiththiscircuit’soperation,wegetthetotalprocessofbinaryadditionsmoothly.Pseudo-randomnumbergeneration–tomodelalinearfeedbackshiftregister,Ex-ORgatesareusedandgeneratearandomsequenceofbits.WantToLearnFaster?🎓Getelectricalarticlesdeliveredtoyourinboxeveryweek.Nocreditcardrequired—it’s100%free.AboutElectrical4UElectrical4Uisdedicatedtotheteachingandsharingofallthingsrelatedtoelectricalandelectronicsengineering....RelatedArticlesTruthTables:WhatAreThey?(Truth…NANDGate:Whatisit?(Working…INHIBITGateDigitalLogicGatesLeaveaCommentCancelreplyCommentNameEmailΔRecentPostsreportthisadPleasefeelfreetocontactusifyou’dliketorequestaspecifictopic.Clickheretoseeourprivacypolicy.WeareaparticipantintheAmazonServicesLLCAssociatesProgram,anaffiliateadvertisingprogramdesignedtoprovideameansforustoearnfeesbylinkingtoAmazon.comandaffiliatedsites.Fulldisclaimerhere.xx