Multiple-input Gates | Logic Gates | Electronics Textbook

As indicated by the truth table, the purpose of an Exclusive-NOR gate is to output a “high” (1) logic level whenever both inputs are at the same logic levels ( ... NetworkSites: Latest News TechnicalArticles Latest Projects Education Latest News TechnicalArticles MarketInsights Education LogIn Join Login JoinAAC Orsigninwith Facebook Google LinkedIn GitHub     0:00 / 0:00 Podcast Latest Subscribe Google Spotify Apple iHeartRadio Stitcher Pandora TuneIn Menu Articles Latest News Projects TechnicalArticles IndustryArticles IndustryWhitePapers Forums Latest HardwareDesign Embedded&Programming Education Math&Science Community Education Textbooks VideoLectures&Tutorials Worksheets IndustryWebinars VirtualWorkshops Tools Calculators PartSearch TestEquipmentDatabase BomTool ICDesignCenter Videos Latest NewProducts VideoTutorials On-DemandWebinars TechChats VirtualWorkshops Datasheets Giveaways Industry Tech Days Podcast Connectwithus NetworkSites: Textbook Multiple-inputGates JoinourEngineeringCommunity!Sign-inwith: 1 Home Textbook Vol.IV-Digital LogicGates Multiple-inputGates PagesinChapter3 DigitalSignalsandGates TheNOTGate The“Buffer”Gate Multiple-inputGates TTLNANDandANDgates TTLNORandORgates CMOSGateCircuitry Special-outputGates GateUniversality LogicSignalVoltageLevels DIPGatePackaging Multiple-inputGates Chapter3-LogicGates PDFVersion TheUseofLogicGate Invertersandbuffersexhaustthepossibilitiesforsingle-inputgatecircuits.Whatmorecanbedonewithasinglelogicsignalbuttobufferitorinvertit?Toexploremorelogicgatepossibilities,wemustaddmoreinputterminalstothecircuit(s). Addingmoreinputterminalstoalogicgateincreasesthenumberofinputstatepossibilities.Withasingle-inputgatesuchastheinverterorbuffer,therecanonlybetwopossibleinputstates:eithertheinputis“high”(1)oritis“low”(0). Aswasmentionedpreviouslyinthischapter,atwoinputgatehasfourpossibilities(00,01,10,and11).Athree-inputgatehaseightpossibilities(000,001,010,011,100,101,110,and111)forinputstates. Thenumberofpossibleinputstatesisequaltotwotothepowerofthenumberofinputs:       Thisincreaseinthenumberofpossibleinputstatesobviouslyallowsformorecomplexgatebehavior.Now,insteadofmerelyinvertingoramplifying(buffering)asingle“high”or“low”logiclevel,theoutputofthegatewillbedeterminedbywhatevercombinationof1’sand0’sispresentattheinputterminals. Sincesomanycombinationsarepossiblewithjustafewinputterminals,therearemanydifferenttypesofmultiple-inputgates,unlikesingle-inputgateswhichcanonlybeinvertersorbuffers.Eachbasicgatetypewillbepresentedinthissection,showingitsstandardsymbol,truthtable,andpracticaloperation.TheactualTTLcircuitryofthesedifferentgateswillbeexploredinsubsequentsections. TheANDGate Oneoftheeasiestmultiple-inputgatestounderstandistheANDgate,so-calledbecausetheoutputofthisgatewillbe“high”(1)ifandonlyifallinputs(firstinputandthesecondinputand...)are“high”(1).Ifanyinput(s)is“low”(0),theoutputisguaranteedtobeina“low”stateaswell.       Incaseyoumighthavebeenwondering,ANDgatesaremadewithmorethanthreeinputs,butthisislesscommonthanthesimpletwo-inputvariety.   Two-inputANDGate’sTruthTable Atwo-inputANDgate’struthtablelookslikethis:     ANDGateSampleCircuitOperation Whatthistruthtablemeansinpracticaltermsisshowninthefollowingsequenceofillustrations,withthe2-inputANDgatesubjectedtoallpossibilitiesofinputlogiclevels.AnLED(Light-EmittingDiode)providesvisualindicationoftheoutputlogiclevel:               Itisonlywithallinputsraisedto“high”logiclevelsthattheANDgate’soutputgoes“high,”thusenergizingtheLEDforonlyoneoutofthefourinputcombinationstates.   TheNANDGate AvariationontheideaoftheANDgateiscalledtheNANDgate.Theword“NAND”isaverbalcontractionofthewordsNOTandAND. Essentially,aNANDgatebehavesthesameasanANDgatewithaNOT(inverter)gateconnectedtotheoutputterminal.Tosymbolizethisoutputsignalinversion,theNANDgatesymbolhasabubbleontheoutputline. ThetruthtableforaNANDgateisasonemightexpect,exactlyoppositeasthatofanANDgate:       AswithANDgates,NANDgatesaremadewithmorethantwoinputs.Insuchcases,thesamegeneralprincipleapplies:theoutputwillbe“low”(0)ifandonlyifallinputsare“high”(1).Ifanyinputis“low”(0),theoutputwillgo“high”(1).   TheORGate OurnextgatetoinvestigateistheORgate,so-calledbecausetheoutputofthisgatewillbe“high”(1)ifanyoftheinputs(firstinputorthesecondinputor...)are“high”(1).TheoutputofanORgategoes“low”(0)ifandonlyifallinputsare“low”(0).     Two-inputORGateTruthTable   Atwo-inputORgate’struthtablelookslikethis:       ORGateSampleCircuitOperation   ThefollowingsequenceofillustrationsdemonstratestheORgate’sfunction,withthe2-inputsexperiencingallpossiblelogiclevels.AnLED(Light-EmittingDiode)providesvisualindicationofthegate’soutputlogiclevel:                   Aconditionofanyinputbeingraisedtoa“high”logiclevelmakestheORgate’soutputgo“high,”thusenergizingtheLEDforthreeoutofthefourinputcombinationstates. TheNORGate Asyoumighthavesuspected,theNORgateisanORgatewithitsoutputinverted,justlikeaNANDgateisanANDgatewithaninvertedoutput.       NORgates,likealltheothermultiple-inputgatesseenthusfar,canbemanufacturedwithmorethantwoinputs.Still,thesamelogicalprincipleapplies:theoutputgoes“low”(0)ifanyoftheinputsaremade“high”(1).Theoutputis“high”(1)onlywhenallinputsare“low”(0).   TheNegative-ANDGate ANegative-ANDgatefunctionsthesameasanANDgatewithallitsinputsinverted(connectedthroughNOTgates).Inkeepingwithstandardgatesymbolconvention,theseinvertedinputsaresignifiedbybubbles. Contrarytomostpeoples’firstinstinct,thelogicalbehaviorofaNegative-ANDgateisnotthesameasaNANDgate.Itstruthtable,actually,isidenticaltoaNORgate:     TheNegative-ORGate   Followingthesamepattern,aNegative-ORgatefunctionsthesameasanORgatewithallitsinputsinverted.Inkeepingwithstandardgatesymbolconvention,theseinvertedinputsaresignifiedbybubbles.ThebehaviorandtruthtableofaNegative-ORgateisthesameasforaNANDgate:     TheExclusive-ORGate   Thelastsixgatetypesareallfairlydirectvariationsonthreebasicfunctions:AND,OR,andNOT.TheExclusive-ORgate,however,issomethingquitedifferent. Exclusive-ORgatesoutputa“high”(1)logicleveliftheinputsareatdifferentlogiclevels,either0and1or1and0.Conversely,theyoutputa“low”(0)logicleveliftheinputsareatthesamelogiclevels. TheExclusive-OR(sometimescalledXOR)gatehasbothasymbolandatruthtablepatternthatisunique:     XOREquivalentCircuits   ThereareequivalentcircuitsforanExclusive-ORgatemadeupofAND,OR,andNOTgates,justastherewereforNAND,NOR,andthenegative-inputgates.AratherdirectapproachtosimulatinganExclusive-ORgateistostartwitharegularORgate,thenaddadditionalgatestoinhibittheoutputfromgoing“high”(1)whenbothinputsare“high”(1):       Inthiscircuit,thefinalANDgateactsasabufferfortheoutputoftheORgatewhenevertheNANDgate’soutputishigh,whichitisforthefirstthreeinputstatecombinations(00,01,and10).However,whenbothinputsare“high”(1),theNANDgateoutputsa“low”(0)logiclevel,whichforcesthefinalANDgatetoproducea“low”(0)output. AnotherequivalentcircuitfortheExclusive-ORgateusesastrategyoftwoANDgateswithinverters,setuptogenerate“high”(1)outputsforinputconditions01and10.AfinalORgatethenallowseitheroftheANDgates’“high”outputstocreateafinal“high”output:     Exclusive-ORgatesareveryusefulforcircuitswheretwoormorebinarynumbersaretobecomparedbit-for-bit,andalsoforerrordetection(paritycheck)andcodeconversion(binarytoGreyandviceversa).   TheExclusive-NORGate Finally,ourlastgateforanalysisistheExclusive-NORgate,otherwiseknownastheXNORgate.ItisequivalenttoanExclusive-ORgatewithaninvertedoutput.ThetruthtableforthisgateisexactlyoppositeasthatoftheExclusive-ORgate:       Asindicatedbythetruthtable,thepurposeofanExclusive-NORgateistooutputa“high”(1)logiclevelwheneverbothinputsareatthesamelogiclevels(either00or11).   REVIEW: RuleforanANDgate:outputis“high”onlyiffirstinputandsecondinputareboth“high.” RuleforanORgate:outputis“high”ifinputAorinputBare“high.” RuleforaNANDgate:outputisnot“high”ifboththefirstinputandthesecondinputare“high.” RuleforaNORgate:outputisnot“high”ifeitherthefirstinputorthesecondinputare“high.” ANegative-ANDgatebehaveslikeaNORgate. ANegative-ORgatebehaveslikeaNANDgate. RuleforanExclusive-ORgate:outputis“high”iftheinputlogiclevelsaredifferent. RuleforanExclusive-NORgate:outputis“high”iftheinputlogiclevelsarethesame.   RELATEDWORKSHEETS: BasicLogicGatesWorksheet BooleanAlgebraWorksheet The“Buffer”Gate TextbookIndex TTLNANDandANDgates RelatedContent GateDriverSolutionsforFastSwitchingApplications HalfBridgeandGateDriveMeasurementsandTechniques UniversalLogicGates CombinationalLogicCircuitDesignandSimulationUsingGates LairdSentriusRG1LoRa-EnabledGateway|NewProductBrief PublishedunderthetermsandconditionsoftheDesignScienceLicense Comments 1Comment Logintocomment V VictorEgwurube April08,2021 Nicereallyhelped Like. 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