NAND and NOR implementation - BrainKart

Any logic function can be implemented using NAND gates. To achieve this, first the logic function has to be written in Sum of Product (SOP) form ... Togglenavigation BrainKart.com HOME AnnaUniversity AnnaUniversity EEE ECE Civil MECH CSE IT GATEExam TANCETAnnaUniv AnnaUniv JEEIEEE Medical MBBS Nursing BPharm Medical MD Medical MGRUniversity NEET AIIMS Engineering Engineering Electrical Electronics Civil Mechanical ComputerScience InformationTechnology GATEExam TANCETAnnaUniv AnnaUniversity JEEIEEE MBA MBA AnnaUnivMBA CAT TNSchool TamilNaduSchool TN12thStd TN11thStd TN10thStd TN9thStd TN1markTest JEEIEEE NEET AIIMS EntranceExam AllExams UPSCCivilservices GATEExam JEEIEEE NEET AIIMS CAT CLAT Banking UGCNET TANCETAnnaUniv More BasicScience BioTech Botany Aqua BDS InstallApp Contact Policy Home||DigitalPrinciplesandSystemDesign|NANDandNORimplementation PrevPageNextPage   PostedOn: 29.11.201612:34am Chapter:DigitalPrinciplesandSystemDesign:BooleanAlgebraandLogicGates NANDandNORimplementation AnylogicfunctioncanbeimplementedusingNANDgates.Toachievethis,firstthelogicfunctionhastobewritteninSumofProduct(SOP)form.OncelogicfunctionisconvertedtoSOP,thenisveryeasytoimplementusingNANDgate. NANDandNORimplementation   AnylogicfunctioncanbeimplementedusingNANDgates.To achievethis,firstthelogicfunctionhastobewritteninSumofProduct (SOP)form.OncelogicfunctionisconvertedtoSOP,thenisveryeasyto implementusingNANDgate.InotherwordsanylogiccircuitwithANDgatesin firstlevelandORgatesinsecondlevelcanbeconvertedintoaNAND-NANDgate circuit.   Consider thefollowingSOPexpression F=W.X.Y +X.Y.Z+Y.Z.W   TheaboveexpressioncanbeimplementedwiththreeANDgates infirststageandoneORgateinsecondstageasshowninfigure.    IfbubblesareintroducedatAND gatesoutputandORgatesinputs(thesameforNORgates),theabovecircuit becomesasshowninfigure. NowreplaceORgatewithinput bubblewiththeNANDgate.Nowwehavecircuitwhichisfullyimplementedwith justNANDgates.   ü     RealizationoflogicgatesusingNANDgates   Implementing aninverterusingNANDgate       ü    RealizationoflogicfunctionusingNORgates   AnylogicfunctioncanbeimplementedusingNORgates.To achievethis,firstthelogicfunctionhastobewritteninProductofSum (POS)form.OnceitisconvertedtoPOS,thenit'sveryeasytoimplementusing NORgate.InotherwordsanylogiccircuitwithORgatesinfirstlevelandAND gatesinsecondlevelcanbeconvertedintoaNOR-NORgatecircuit.   Consider thefollowingPOSexpression   F=(X+Y) .(Y+Z) TheaboveexpressioncanbeimplementedwiththreeORgatesin firststageandoneANDgateinsecondstageasshowninfigure. IfbubbleareintroducedattheoutputoftheORgatesandthe inputsofANDgate,theabovecircuitbecomesasshowninfigure.   NowreplaceANDgatewithinputbubblewiththeNORgate.Now wehavecircuitwhichisfullyimplementedwithjustNORgates. Minimization Technique   Theprimaryobjectiveofallsimplificationproceduresisto obtainanexpressionthathastheminimumnumberofterms.Obtainingan expressionwiththeminimumnumberofliteralsisusuallythesecondary objective.Ifthereismorethanonepossiblesolutionwiththesamenumberof terms,theonehavingtheminimumnumberofliteralsisthechoice.   ThereareseveralmethodsforsimplificationofBooleanlogic expressions.Theprocessisusuallycalledlogicminimizationandthegoalis toformaresultwhichisefficient.Twomethodswewilldiscussarealgebraic minimizationandKarnaughmaps.Forverycomplicatedproblemstheformermethod canbedoneusingspecialsoftwareanalysisprograms.Karnaughmapsarealso limitedtoproblemswithupto4binaryinputs.TheQuine–McCluskey tabularmethodisusedformorethan4binaryinputs.  Ref: 1)  A.P  Godse  &  D.A  Godse  “Digital  Electronics”,  Technical  publications,  Pune, Revised edition,2008.Pg.No:3.782)  Morris  Mano  M.  and  Michael  D.  Ciletti,  “Digital  Design”,  IV  Edition,  Pearson Edition 2008.Pg.No:89.PrevPageNextPage StudyMaterial,LecturingNotes,Assignment,Reference,Wikidescriptionexplanation,briefdetailDigitalPrinciplesandSystemDesign:BooleanAlgebraandLogicGates:NANDandNORimplementation| PrevPageNextPage RelatedTopics DigitalPrinciplesandSystemDesignAnnaUniversity-AllSubjectsAnnaUniversityCSE-AllSubjectsAnnaUniversityIT-AllSubjectsDigitalPrinciplesandSystemDesign:BooleanAlgebraandLogicGatesBooleanAlgebraandLogicGatesBooleanAlgebraandLogicGates-Pre-RequisiteDiscussionReviewofNumberSystemsArithmeticOperationsBinarycodesBooleanAlgebraandTheoremsDigitalLogicGatesNANDandNORimplementationKarnaughMapsQuine-MccluskeyMethodorTabularmethodofminimizationoflogicfunctionsImportantShortQuestionsAnswers:BooleanAlgebraandLogicGatesGlossaryTechnicalTerms:BooleanAlgebraandLogicGates PrivacyPolicy, TermsandConditions, DMCAPolicyandCompliant Copyright©2018-2023BrainKart.com;AllRightsReserved.DevelopedbyTherithalinfo,Chennai.