Boolean Algebra Truth Tables for Logic Gate Functions

The table used to represent the boolean expression of a logic gate function is commonly called a Truth Table. A logic gate truth table shows each possible ... X Registertodownloadpremiumcontent! Registertodownloadpremiumcontent! X Deutsch Polski Register LogIn ACCircuits Amplifiers Attenuators BinaryNumbers BooleanAlgebra Capacitors CombinationalLogic Connectivity Counters DCCircuits Diodes Electromagnetism Filters Inductors Input/OutputDevices LogicGates MiscellaneousCircuits OperationalAmplifiers Oscillator PowerElectronics PowerSupplies Premium RCNetworks Resistors Resources SequentialLogic Systems Transformers Transistors Uncategorized WaveformGenerators PremiumContent FurtherEducation Sitemap ContactUs Home / BooleanAlgebra / BooleanAlgebraTruthTables BooleanAlgebraTruthTables BooleanAlgebraExpressionscanbeusedtoconstructdigitallogictruthtablesfortheirrespectivefunctions AswellasastandardBooleanExpression,theinputandoutputinformationofanyLogicGateorcircuitcanbeplottedintoastandardtabletogiveavisualrepresentationoftheswitchingfunctionofthesystem. ThetableusedtorepresentthebooleanexpressionofalogicgatefunctioniscommonlycalledaTruthTable.Alogicgatetruthtableshowseachpossibleinputcombinationtothegateorcircuitwiththeresultantoutputdependinguponthecombinationoftheseinput(s). Forexample,considerasingle2-inputlogiccircuitwithinputvariableslabelledasAandB.Thereare“four”possibleinputcombinationsor22of“OFF”and“ON”forthetwoinputs.However,whendealingwithBooleanexpressionsandespeciallylogicgatetruthtables,wedonotgeneraluse“ON”or“OFF”butinsteadgivethembitvalueswhichrepresentalogiclevel“1”oralogiclevel“0”respectively. ThenthefourpossiblecombinationsofAandBfora2-inputlogicgateisgivenas: InputCombination1.–“OFF”–“OFF”or( 0,0 ) InputCombination2.–“OFF”–“ON”or( 0,1 ) InputCombination3.–“ON”–“OFF”or( 1,0 ) InputCombination4.–“ON”–“ON”or( 1,1 ) Therefore,a3-inputlogiccircuitwouldhave8possibleinputcombinationsor23anda4-inputlogiccircuitwouldhave16or24,andsoonasthenumberofinputsincreases.Thenalogiccircuitwith“n”numberofinputswouldhave2npossibleinputcombinationsofboth“OFF”and“ON”. Soinordertokeepthingssimpletounderstand,inthistutorialwewillonlydealwithstandard2-inputtypelogicgates,buttheprincipalsarestillthesameforgateswithmorethantwoinputs. ThentheTruthtablesfora2-inputANDGate,a2-inputORGateandasingleinputNOTGatearegivenas: 2-inputANDGate Fora2-inputANDgate,theoutputQistrueifBOTHinputA“AND”inputBarebothtrue,givingtheBooleanExpressionof:( Q=AandB ). Symbol TruthTable A B Q 0 0 0 0 1 0 1 0 0 1 1 1 BooleanExpressionQ=A.B ReadasAANDBgivesQ NotethattheBooleanExpressionforatwoinputANDgatecanbewrittenas:A.BorjustsimplyABwithoutthedecimalpoint. 2-inputOR(InclusiveOR)Gate Fora2-inputORgate,theoutputQistrueifEITHERinputA“OR”inputBistrue,givingtheBooleanExpressionof:( Q=AorB ). Symbol TruthTable A B Q 0 0 0 0 1 1 1 0 1 1 1 1 BooleanExpressionQ=A+B ReadasAORBgivesQ NOTGate(Inverter) ForasingleinputNOTgate,theoutputQisONLYtruewhentheinputis“NOT”true,theoutputistheinverseorcomplementoftheinputgivingtheBooleanExpressionof:( Q=NOTA ). Symbol TruthTable A Q 0 1 1 0 BooleanExpressionQ=NOTAorA ReadasinversionofAgivesQ TheNANDandtheNORGatesareacombinationoftheANDandORGatesrespectivelywiththatofaNOTGate(inverter). 2-inputNAND(NotAND)Gate Fora2-inputNANDgate,theoutputQisNOTtrueifBOTHinputAandinputBaretrue,givingtheBooleanExpressionof:( Q=not(AANDB) ). Symbol TruthTable A B Q 0 0 1 0 1 1 1 0 1 1 1 0 BooleanExpressionQ=A.B ReadasAANDBgivesNOT-Q 2-inputNOR(NotOR)Gate Fora2-inputNORgate,theoutputQistrueifBOTHinputAandinputBareNOTtrue,givingtheBooleanExpressionof:( Q=not(AORB) ). Symbol TruthTable A B Q 0 0 1 0 1 0 1 0 0 1 1 0 BooleanExpressionQ=A+B ReadasAORBgivesNOT-Q AswellasthestandardlogicgatestherearealsotwospecialtypesoflogicgatefunctioncalledanExclusive-ORGateandanExclusive-NORGate.TheBooleanexpressiontoindicateanExclusive-ORorExclusive-NORfunctionistoasymbolwithaplussigninsideacircle,( ⊕ ). Theswitchingactionsofbothofthesetypesofgatescanbecreatedusingtheabovestandardlogicgates.However,astheyarewidelyusedfunctionstheyarenowavailableinstandardICformandhavebeenincludedhereasreference. 2-inputEX-OR(ExclusiveOR)Gate Fora2-inputEx-ORgate,theoutputQistrueifEITHERinputAorifinputBistrue,butNOTbothgivingtheBooleanExpressionof:( Q=(AandNOTB)or(NOTAandB) ). Symbol TruthTable A B Q 0 0 0 0 1 1 1 0 1 1 1 0 BooleanExpressionQ=A ⊕ B   2-inputEX-NOR(ExclusiveNOR)Gate Fora2-inputEx-NORgate,theoutputQistrueifBOTHinputAandinputBarethesame,eithertrueorfalse,givingtheBooleanExpressionof:( Q=(AandB)or(NOTAandNOTB) ). Symbol TruthTable A B Q 0 0 1 0 1 0 1 0 0 1 1 1 BooleanExpressionQ=A ⊕ B   Summaryof2-inputLogicGates ThefollowingTruthTablecomparesthelogicalfunctionsofthe2-inputlogicgatesabove. Inputs TruthTableOutputsForEachGate A B AND NAND OR NOR EX-OR EX-NOR 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 ThefollowingtablegivesalistofthecommonlogicfunctionsandtheirequivalentBooleannotation. LogicFunction BooleanNotation AND A.B OR A+B NOT A NAND A.B NOR A+B EX-OR (A.B) + (A.B)orA ⊕ B EX-NOR (A.B) + (A.B) or A ⊕ B 2-inputlogicgatetruthtablesaregivenhereasexamplesoftheoperationofeachlogicfunction,buttherearemanymorelogicgateswith3,4even8individualinputs.Themultipleinputgatesarenodifferenttothesimple2-inputgatesabove,Soa4-inputANDgatewouldstillrequireALL4-inputstobepresenttoproducetherequiredoutputatQanditslargertruthtablewouldreflectthat. PreviousLawsofBooleanAlgebra NextBooleanAlgebraExamples ReadmoreTutorialsinBooleanAlgebra 1.LogicANDFunction 2.LogicORFunction 3.LogicNOTFunction 4.LogicNANDFunction 5.LogicNORFunction 6.LawsofBooleanAlgebra 7.BooleanAlgebraTruthTables 8.BooleanAlgebraExamples 9.DeMorgan’sTheorem 10.SwitchingTheory 11.SumofProduct 12.ProductofSum 489Comments JointheconversationCancelreplyError!Pleasefillallfields. Notifymeoffollow-upcommentsbyemail. Δ Mikemwila Pleasesomeofusaccessingthisinformationwearestudentsoputtheprovisionofreferences PostedonJuly12th2022|12:57am Reply HellenChepkirui Iappreciate PostedonJune12th2022|12:47pm Reply Livio IneedtounderstandthePOSandsop PostedonJune07th2022|6:17am Reply Yakubusuleiman Iwillliketosaythanks*forhelpingandineedtounderstoodthemethodsverywellthanks🙏 PostedonJune04th2022|11:15am Reply Victor Beautiful PostedonMay30th2022|8:17am Reply chummiestreetwaider Ineedmoreexplanationonthis PostedonMay24th2022|7:32am Reply JohnDoe You’resusmydrilla PostedonMay27th2022|12:16am Reply ALIA DevelopthetruthtableforthefollowingBooleanexpression: C=~A+(AB) PostedonMay18th2022|3:26pm Reply Meghana.r CanuexplainusabtNANDasOR,AND,NOTgayee PostedonMay13th2022|9:10am Reply WayneStorr ThenpleasemakeanefforttoreadtheLogicgatetutorialssectionabtNANDasOR,AND,NOTgayee PostedonMay13th2022|9:30am Reply GoodnessSalvation Interesting PostedonMay11th2022|11:18am Reply NAFIUYUSUF EVERYTHINGISDONE PostedonMay08th2022|8:57pm Reply Muhammadhauwaum Weareveryinterestedwiththisexplanations PostedonMay07th2022|6:27pm Reply KatongoChoongo Forthefollowingfunctions,constructatruthtableanddrawalogiccircuitdiagram. a.y(A,B)=(AB)’+B’ b.y(A,B,C)=(A+B)’C c.y(A,B)=A’+B d.y(A,B,C)=((A+B)'(B+C)’)’ PostedonApril16th2022|10:03pm Reply NeetuKumari Verynice PostedonJuly11th2022|5:01pm Reply ezra hello PostedonApril11th2022|12:54pm Reply Ismaul Booleanalgebra PostedonApril07th2022|9:56am Reply JohnAgustin AnyonecananswerthisoneF=(a+b)(a+c)+(b.c) PostedonApril05th2022|2:45am Reply WayneStorr F=(A+B)(A+C)+BC F=A+BC PostedonApril05th2022|11:00am Reply BonifaceKaiserChelluget Dohelpfultutorial PostedonMarch26th2022|3:52am Reply Hilonee F=ABC+A’BC+B’C’ PostedonMarch16th2022|5:05pm Reply Zmonsta F=ABC+A’BC+B’C’ =BC(A+A’)+B’C =BC(1)+B’C’(AdditivetheoremA+A’=1) =BC+B’C’(ExclusiveNor) =BEX-NORC PostedonMarch22nd2022|3:59am Reply Victor It’sgoodtobehomeofautomobileelectricianhopefullyandinteresting.Iwanttolearnmoreaboutit PostedonMarch12th2022|1:18pm Reply Karinamwaba Thankssomuch,Istillneedtolearnsomemore. PostedonMarch05th2022|4:23am Reply Tijaniarome Ineedmoreaboutthislogicgateandtruetable PostedonFebruary24th2022|5:22am Reply ViewMore ReadmoreTutorialsinBooleanAlgebra 1.LogicANDFunction 2.LogicORFunction 3.LogicNOTFunction 4.LogicNANDFunction 5.LogicNORFunction 6.LawsofBooleanAlgebra 7.BooleanAlgebraTruthTables 8.BooleanAlgebraExamples 9.DeMorgan’sTheorem 10.SwitchingTheory 11.SumofProduct 12.ProductofSum LookingforDataSheets? Close TheBasics ContactUs PrivacyPolicy TermsofUse ForAdvertisers ContactSales MediaGuideRequest AspencoreNetwork EDN EETimes EEWeb ElectronicProducts PowerElectronicsNews EPSNews Embedded PlanetAnalog ElectroSchematics TechOnline Datasheets.com ElectronicsKnowHow IoTTimes GlobalNetwork EETimesAsia EETimesChina EETimesIndia EETimesJapan EETimesTaiwan EDNAsia EDNChina EDNTaiwan EDNJapan ESMChina ConnectwithUs Facebook AllcontentsareCopyright©2022byAspenCore,Inc.Allrightsreserved. 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