Basic Logic Gates - Types, Functions, Truth Table ... - Byju's

Logic gates are the electronic circuits in a digital system that are mainly based on the Boolean function. Learn about AND, OR, XOR, NOT, NAND, NOR, ... CheckoutJEEMAINS2022QuestionPaperAnalysis: CheckoutJEEMAINS2022QuestionPaperAnalysis: × DownloadNow JEEIITJEEStudyMaterialBasicLogicGates Previous Next BasicLogicGates Logicgatesareanimportantconceptifyouarestudyingelectronics.TheseareimportantdigitaldevicesthataremainlybasedontheBooleanfunction.Logicgatesareusedtocarryoutlogicaloperationsonsingleormultiplebinaryinputsandgiveonebinaryoutput.Insimpleterms,logicgatesaretheelectroniccircuitsinadigitalsystem. Inthislesson,wewillfurtherlookatthedifferenttypesofbasiclogicgateswiththeirtruthtableandunderstandwhateachoneisdesignedfor. TableofContent TypesofBasicLogicGates ApplicationOfLogicGates DeMorgan’sTheorem ImportantConversions TypesofBasicLogicGates Thereareseveralbasiclogicgatesusedinperformingoperationsindigitalsystems.Thecommononesare; ORGate ANDGate NOTGate XORGate Additionally,thesegatescanalsobefoundinacombinationofoneortwo.ThereforewegetothergatessuchasNANDGate,NORGate,EXORGate,EXNORGate. AlsoRead:Transistor ORGate InORgatetheoutputofanORgateattainsthestate1ifoneormoreinputsattainthestate1.   TheBooleanexpressionofORgateisY=A+B,readasYequalsA‘OR’B. Thetruthtableofatwo-inputORbasicgateisgivenas; A B Y 0 0 0 0 1 1 1 0 1 1 1 1 ANDGate InANDgatetheoutputofanANDgateattainsthestate1ifandonlyifalltheinputsareinstate1.   TheBooleanexpressionofANDgateisY=A.B Thetruthtableofatwo-inputANDbasicgateisgivenas; A B Y 0 0 0 0 1 0 1 0 0 1 1 1 NOTGate InNOTgatetheoutputofaNOTgateattainsthestate1ifandonlyiftheinputdoesnotattainthestate1.     TheBooleanexpressionis Y=\(\begin{array}{l}\bar{A}\end{array}\),readasYequalsNOTA. ThetruthtableofNOTgateisasfollows; A Y 0 1 1 0 Thethreegates(OR,ANDandNOT),whenconnectedinvariouscombinations,giveusbasiclogicgatessuchasNAND,NORgates,whicharetheuniversalbuildingblocksofdigitalcircuits. NANDGate ThisbasiclogicgateisthecombinationofANDandNOTgate.   TheBooleanexpressionofNANDgateis Y=\(\begin{array}{l}\bar{A.B}\end{array}\) ThetruthtableofaNANDgateisgivenas; A B Y 0 0 1 0 1 1 1 0 1 1 1 0 NORGate ThisgateisthecombinationofORandNOTgate.     TheBooleanexpressionofNORgateis Y=\(\begin{array}{l}\bar{A+B}\end{array}\) ThetruthtableofaNORgateisasfollows; A B Y 0 0 1 0 1 0 1 0 0 1 1 0 Exclusive-ORgate(XORGate) InXORgatetheoutputofatwo-inputXORgateattainsthestate1ifoneaddsonlyinputattainsthestate1.     TheBooleanexpressionoftheXORgateis\(\begin{array}{l}A.\bar{B}+\bar{A}.B\end{array}\) or \(\begin{array}{l}Y=A\bigoplusB\end{array}\) ThetruthtableofanXORgateis; A B Y 0 0 0 0 1 1 1 0 1 1 1 0 Exclusive-NORGate(XNORGate) InXNORgatetheoutputisinstate1whenitsbothinputsarethesamethatis,both0orboth1.   TheBooleanexpressionofXNORgate  ThetruthtableofanXNORgateisgivenbelow; A B Y 0 0 1 0 1 0 1 0 0 1 1 1 ApplicationOfLogicGates Logicgateshavealotofapplicationsbuttheyaremainlybasedupontheirmodeofoperationsortheirtruthtable.Basiclogicgatesareoftenfoundincircuitssuchassafetythermostat,push-buttonlock,automaticwateringsystem,light-activatedburglaralarmandmanyotherelectronicdevices. Oneoftheprimarybenefitsisthatbasiclogicgatescanbeusedinamixtureofdifferentcombinationsiftheoperationsareadvanced.Besides,thereisnolimittothenumberofgatesthatcanbeusedinasingledevice.However,itcanberestrictedduetothegivenphysicalspaceinthedevice.Indigitalintegratedcircuits(ICs)wewillfindanarrayofthelogicgateareaunit. DeMorgan’sTheorem Firsttheorem– ItstatesthattheNANDgateis equivalent toabubbledORgate. \(\begin{array}{l}\bar{A.B}=\bar{A}+\bar{B}\end{array}\) Secondtheorem– ItstatesthattheNORgateis equivalent toabubbledANDgate. \(\begin{array}{l}\overline{A+B}=\bar{A}.\bar{B}\end{array}\) ImportantConversions 1) The‘NAND’gate: From‘AND’and‘NOT’gate.   Booleanexpressionandtruthtable: Y=A⋅B¯¯¯¯¯¯¯¯¯¯¯ A B Y′=A⋅B Y 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 (2) The‘NOR’gate: From‘OR’and‘NOT’gate   Booleanexpressionandtruthtable: Y=A+B A B Y′=A+B Y 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 (3) The‘XOR’gate: From‘NOT’,‘AND’and ‘OR’gate. Thelogicgatewhichgiveshighoutput(i.e.,1)ifeitherinputAorinputBbutnotbotharehigh(i.e.1)iscalledexclusiveORgateortheXORgate.ItmaybenotedthatifboththeinputsoftheXORgatearehigh,thentheoutputislow(i.e.,0).     Booleanexpressionandtruthtable: \(\begin{array}{l}A.\bar{B}+\bar{A}.B\end{array}\) or \(\begin{array}{l}Y=A\bigoplusB\end{array}\) A B Y 0 0 0 0 1 1 1 0 1 1 1 0 (4)TheExclusivenor(XNOR)gateXOR+NOT   Booleanexpression: \(\begin{array}{l}Y=\bar{(A\bigoplusB)}\end{array}\)   A B Output 0 0 1 0 1 0 1 0 0 1 1 1   FrequentlyAskedQuestionsonBasicLogicGatesWhatistheuseofbasiclogicgates? Fundamentallogicalfunctionsareperformedusingbasiclogicgates.Thesearethefundamentalcomponentsofintegratedcircuits. Whatarethetypesofbasiclogicgates? ANDgate,ORgate,XORgate,NANDgate,NORgate,XNORgate,andNOTgatearetheseventypesofbasiclogicgates. Whatareuniversalgates? AuniversalgateisalogicgatethatcanimplementanyBooleanfunctionwithouthavingtheusageofanotherlogicgate.TheuniversalgatesaretheNORandNANDgates. TestyourKnowledgeonBasicLogicGates Q5 PutyourunderstandingofthisconcepttotestbyansweringafewMCQs.Click‘StartQuiz’tobegin! Selectthecorrectanswerandclickonthe“Finish”buttonCheckyourscoreandanswersattheendofthequiz StartQuiz Congrats! 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