Truth table for a system of four NAND gates as shown in figure is

Hint: Any complicated circuit should first be solved by solving it algebraically with the help of the laws given in Boolean algebra. If A and B are two inputs ... ClaimyourFREESeatinVedantuMasterClasses!RegisternowFreeClassesSigninQuestions&AnswersCBSEPhysicsGrade12LogicGatesAnswerTruthtableforasystemoffourNANDgatesasshowninfigureis: A.ABY000011101110B.ABY000010101111C.ABY001011100110D.ABY001010100111AnswerVerified193.5k+viewsHint:AnycomplicatedcircuitshouldfirstbesolvedbysolvingitalgebraicallywiththehelpofthelawsgiveninBooleanalgebra.IfAandBaretwoinputsofaNANDgate,thenitsoutputisgivenbyY=(A.B)’.Formulaused:DeMorgan’slaw:Complementofsumisproductofcomplementandviceversa.Theexpressionsare:(A+B)’=A'.B'(A.B)’=A'+B'Distributivelaw:A+B.C=(A+B)(A+C)TheselawsarespecificallyforBooleanalgebra.Completestepbystepanswer:ANANDgateisalogicgatethathasalogiccircuitwhichproducestheoutputasacomplementofproductsoftwoormoreinputs.ThetruthtableforatwoinputNANDgateisgivenas:ABY=(A.B)’001011101110ItcanbeseenfromthetruthtablethattheNANDgateproducesalowoutputonlywhenbothinputsarehigh.ThetruthtableisjustthecomplementoftheANDgatetruthtable.  Thegivencircuithas4NANDgates.Thesimplificationcanbedoneas:1.FromthefirstNANDgateontheleft,wegetitsoutputas:     (A.B)’      astheinputstothegatewereAandB.2.Thisoutputisconnectedasaninputinthenextstage.TheupperNANDgategives: ((A.B)’.A)’  whichissimplifiedas ((A.B)’.A)’=((A.B)’)’+A'=AB+A'.Usingdistributivelaw,weget:AB+A'=(A+A')(B+A')=B+A'Similarly,thelowerNANDgateproduces:Output:B'+AThelaststageoftheNANDgateproducestheoutput:((B+A')(B'+A))’=(B+A')’+(B'+A)’=A.B'+B.A'ThiscanberecognizedastheexpressionforexclusiveORgate.ThetruthtableforanexclusiveORgateisgivenas:ABY000011101110So,thecorrectansweris“OptionA”.Note:Theinputconnectionsshouldbenoteddowncarefully.Itmightchangetheresultentirelyeveniftheprimedpartismissing.ThetruthtableforNANDgatecanberememberedasthecomplementofANDgatetruthtable. RecentlyUpdatedPagesWhatdoesthetermLOScommunicationmeanNametheclass12physicsCBSEHowdoelectromagneticwavestravelinavacuumclass12physicsCBSEHowaregasparticlesdescribedaccordingtothekineticclass12physicsCBSEAballbouncesto80ofitsoriginalheightWhatfractionclass12physicsCBSEAconcavemirroriskeptasshowninfigureItsprincipalclass12physicsCBSEAparallelbeamoflightentersaclearplasticbeadclass12physicsCBSEWhatdoesthetermLOScommunicationmeanNametheclass12physicsCBSEHowdoelectromagneticwavestravelinavacuumclass12physicsCBSEHowaregasparticlesdescribedaccordingtothekineticclass12physicsCBSEAballbouncesto80ofitsoriginalheightWhatfractionclass12physicsCBSEAconcavemirroriskeptasshowninfigureItsprincipalclass12physicsCBSEAparallelbeamoflightentersaclearplasticbeadclass12physicsCBSE12TrendingdoubtsHowdoyoudefineleastcountforVernierCalipersclass12physicsCBSEThelawsofreflectionholdgoodforAPlanemirrorclass12physicsCBSETheloudnessorsoftnessofasoundisdeterminedbasicallyclass12physicsCBSEWritetheprincipleofworkingofanelectricmotoclass12physicsCBSEStateandexplainCoulombslawinelectrostaticsclass12physicsCBSEWhatistherelationshipbetweenfrequencyandwavelengthclass12physicsCBSEDefineresistanceAllnonmetalsarebadconductorsofheatandelectricityclass12physicsCBSEWhydonttwomagneticlinesofforceintersectwithclass12physicsCBSEHowdoyoudefineleastcountforVernierCalipersclass12physicsCBSEThelawsofreflectionholdgoodforAPlanemirrorclass12physicsCBSETheloudnessorsoftnessofasoundisdeterminedbasicallyclass12physicsCBSEWritetheprincipleofworkingofanelectricmotoclass12physicsCBSEStateandexplainCoulombslawinelectrostaticsclass12physicsCBSEWhatistherelationshipbetweenfrequencyandwavelengthclass12physicsCBSEDefineresistanceAllnonmetalsarebadconductorsofheatandelectricityclass12physicsCBSEWhydonttwomagneticlinesofforceintersectwithclass12physicsCBSE123NCERTBookSolutionsNCERTNCERTSolutionsNCERTSolutionsforClass12MathsNCERTSolutionsforClass12PhysicsNCERTSolutionsforClass12ChemistryNCERTSolutionsforClass12BiologyNCERTSolutionsforClass11MathsNCERTSolutionsforClass11PhysicsNCERTSolutionsforClass11ChemistryNCERTSolutionsforClass11BiologyNCERTSolutionsforClass10MathsNCERTSolutionsforClass10ScienceNCERTSolutionsforClass9MathsNCERTSolutionsforClass9ScienceReferenceBookSolutionsHCVermaSolutionsRDSharmaSolutionsRDSharmaClass10SolutionsRDSharmaClass9SolutionsRSAggarwalSolutionsRSAggarwalClass10SolutionsICSEClass10solutionsLakmirSinghSolutionsTextBookSolutionsImportantFormulasMathFormulaPhysicsFormulaChemistryFormulaQuestionPapersPreviousYearQuestionPaperCBSEPreviousYearQuestionPaperforClass10CBSEPreviousYearQuestionPaperforClass12SamplePaperCBSEClass12SamplePapersCBSEClass10SamplePapersICSEClass10SamplePapersMathsPhysicsChemistryBiologyPracticeQuestionsExamsIITJEENEETAIIMSKVPYKCETCOMEDKBITSATVITEEEOLYMPIADSTATEBOARDSQuickLinksJEECrashCourseNCERTBooksCBSEBoardCBSESyllabusICSEBoardFreeStudyMaterialsQuestion&AnswersRevisionNotesImportantQuestionsWorksheetsChildSafetyTermsandConditionsPrivacyPolicyTollFree:1800-120-456-456Mobile:+91988-660-2456(Mon-Sun:9am-11pmIST)Questions?Chatwithus