Gate Universality | Logic Gates | Electronics Textbook

To make a NOR gate perform the NAND function, we must invert all inputs to the NOR gate as well as the NOR gate's output. For a two-input gate, this requires ... 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 GateUniversality JoinourEngineeringCommunity!Sign-inwith: Home Textbook Vol.IV-Digital LogicGates GateUniversality PagesinChapter3 DigitalSignalsandGates TheNOTGate The“Buffer”Gate Multiple-inputGates TTLNANDandANDgates TTLNORandORgates CMOSGateCircuitry Special-outputGates GateUniversality LogicSignalVoltageLevels DIPGatePackaging GateUniversality Chapter3-LogicGates PDFVersion NANDandNORgatespossessaspecialproperty:theyareuniversal.Thatis,givenenoughgates,eithertypeofgateisabletomimictheoperationofanyothergatetype. Forexample,itispossibletobuildacircuitexhibitingtheORfunctionusingthreeinterconnectedNANDgates.TheabilityforasinglegatetypetobeabletomimicanyothergatetypeisoneenjoyedonlybytheNANDandtheNOR.Infact,digitalcontrolsystemshavebeendesignedaroundnothingbuteitherNANDorNORgates,allthenecessarylogicfunctionsbeingderivedfromcollectionsofinterconnectedNANDsorNORs. Asproofofthisproperty,thissectionwillbedividedintosubsectionsshowinghowallthebasicgatetypesmaybeformedusingonlyNANDsoronlyNORs. ConstructingtheNOTfunction       Asyoucansee,therearetwowaystouseaNANDgateasaninverter,andtwowaystouseaNORgateasaninverter.Eithermethodworks,althoughconnectingTTLinputstogetherincreasestheamountofcurrentloadingtothedrivinggate.ForCMOSgates,commoninputterminalsdecreasestheswitchingspeedofthegateduetoincreasedinputcapacitance.   Invertersarethefundamentaltoolfortransformingonetypeoflogicfunctionintoanother,andsotherewillbemanyinvertersshownintheillustrationstofollow.Inthosediagrams,Iwillonlyshowonemethodofinversion,andthatwillbewheretheunusedNANDgateinputisconnectedto+V(eitherVccorVdd,dependingonwhetherthecircuitisTTLorCMOS)andwheretheunusedinputfortheNORgateisconnectedtoground. Bearinmindthattheotherinversionmethod(connectingbothNANDorNORinputstogether)worksjustaswellfromalogical(1’sand0’s)pointofview,butisundesirablefromthepracticalperspectivesofincreasedcurrentloadingforTTLandincreasedinputcapacitanceforCMOS. Constructingthe“buffer”function BeingthatitisquiteeasytoemployNANDandNORgatestoperformtheinverter(NOT)function,itstandstoreasonthattwosuchstagesofgateswillresultinabufferfunction,wheretheoutputisthesamelogicalstateastheinput.       ConstructingtheANDfunction   TomaketheANDfunctionfromNANDgates,allthatisneededisaninverter(NOT)stageontheoutputofaNANDgate.Thisextrainversion“cancelsout”thefirstNinNAND,leavingtheANDfunction.IttakesalittlemoreworktowrestlethesamefunctionalityoutofNORgates,butitcanbedonebyinverting(“NOT”)alloftheinputstoaNORgate.       ConstructingtheNANDfunction   Itwouldbepointlesstoshowyouhowto“construct”theNANDfunctionusingaNANDgate,sincethereisnothingtodo.TomakeaNORgateperformtheNANDfunction,wemustinvertallinputstotheNORgateaswellastheNORgate’soutput.Foratwo-inputgate,thisrequiresthreemoreNORgatesconnectedasinverters.       ConstructingtheORfunction   InvertingtheoutputofaNORgate(withanotherNORgateconnectedasaninverter)resultsintheORfunction.TheNANDgate,ontheotherhand,requiresinversionofallinputstomimictheORfunction,justasweneededtoinvertallinputsofaNORgatetoobtaintheANDfunction. Rememberthatinversionofallinputstoagateresultsinchangingthatgate’sessentialfunctionfromANDtoOR(orviceversa),plusaninvertedoutput.Thus,withallinputsinverted,aNANDbehavesasanOR,aNORbehavesasanAND,anANDbehavesasaNOR,andanORbehavesasaNAND.InBooleanalgebra,thistransformationisreferredtoasDeMorgan’sTheorem,coveredinmoredetailinalaterchapterofthisbook.       ConstructingtheNORfunction   MuchthesameastheprocedureformakingaNORgatebehaveasaNAND,wemustinvertallinputsandtheoutputtomakeaNANDgatefunctionasaNOR.     REVIEW:   NANDandNORgatesareuniversal:thatis,theyhavetheabilitytomimicanytypeofgate,ifinterconnectedinsufficientnumbers.   RELATEDWORKSHEETS: TTLLogicGatesWorksheet BooleanAlgebraWorksheet Special-outputGates TextbookIndex LogicSignalVoltageLevels RelatedContent UniversalLogicGates GateDriverSolutionsforFastSwitchingApplications HalfBridgeandGateDriveMeasurementsandTechniques CombinationalLogicCircuitDesignandSimulationUsingGates ArduinoInfrared(IR)Control…TheUniversalRemoteControl PublishedunderthetermsandconditionsoftheDesignScienceLicense Comments 0Comments Logintocomment Loadmorecomments YouMayAlsoLike Beamforming:FundamentalstoImplementation byAvnet QualcommLaunchesDigitalChassisTechtoDriveVehicleConnectivity byJakeHertz U.S.LawmakersGiveGreenLightforAdaptiveDrivingBeamHeadlights byTylerCharboneau IonQandHyundaiTeamUpforAutomotiveObjectRecognition byJeffChild InfineonHopestoPackaPunchWithBattery-poweredSensorFusionAlarmDesign byJeffChild WelcomeBack Don'thaveanAACaccount?Createonenow. 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