Implementing NOT, OR, AND into NAND gate

Any Boolean expression can be implemented by NAND-NOR gates. For this, first the expression should be converted into SOP or POS form. Home About Contact Home-icon ElectronDevices _Diodes _Rectifiers _Transistors _Specialsemiconductordevices _Poweranddisplaydevices DigitalElectronics Contents Ticker 6/recent/ticker-posts HomeMinimizationtechniquesNAND–NORimplementations:ImplementingNOT,OR,ANDintoNANDgate,ImplementingNOT,OR,ANDintoNORgate. NAND–NORimplementations:ImplementingNOT,OR,ANDintoNANDgate,ImplementingNOT,OR,ANDintoNORgate. October14,2021  NAND–NORimplementations:AnyBooleanexpressioncanbeimplementedbyNAND-NORgates.Forthis,firsttheexpressionshouldbeconvertedintoSOPorPOSform.NANDandNORgatesarecalledasuniversalgatesandtheBooleanexpressioncanbeimplementedwithouttheuseofanyothergates. AnylogiccircuitisconvertedintoNAND-NORcircuitbecausetheyarewidelyusedcommerciallybecauseofitswiredlogic.WiredlogicmeansNORgateisnotphysicallyusedbutusingjustwiresthislogiccanbeobtained.NAND-NORimplementationreducesthenumberofgatesandreducesthesizeofthecircuit.Thisinturnreducestheimplementationcostandthepowerconsumption.AnotherreasonisthefabricationprocessofNANDandNORgateisveryeasyanditisoflowcost.ImplementingNOT,OR,ANDintoNANDgate:ImplementingNOTgateusingNANDgate:(A.A)'=A'  (IdempotentLaw) ImplementingNOTGateusingNANDGateImplementingANDgateusingNANDgate:((AB)'(AB)')'=((AB)')'  (ByIdempotentLaw)   =AB     (InvolutionLaw) ImplementingANDGateusingNANDGateImplementingORgateusingNANDgate:((AA)'(BB)')'=(A'B')'  (ByIdempotentLaw)         =A''+B''  (ByDeMorgan’sLaw)  =A+B   (ByinvolutionLaw)ImplementingORGateusingNANDGateImplementingNOT,OR,ANDintoNORgate:ImplementingNOTgateusingNORgate:(A+A)'=A'  (ByIdempotentLaw)ImplementationofNOTGateusingNORGate ImplementingORgateusingNORgate:((A+A)'+(B+B)')'=(A'+B')'  (ByIdempotentLaw)              =A''.B''  (ByDeMorgan’sLaw)      =A.B   (ByinvolutionLaw)ImplementingORGateusingNORGate ImplementingANDgateusingNORgate:((A+A)'(B+B)')'=(A'+B')'  (ByIdempotentLaw)        =A''.B''  (ByDeMorgan’sLaw) =A.B   (ByinvolutionLaw) ImplementingANDGateusingNORGateEquivalentGates:1) NANDgateisequivalenttotheinvertedinputORgate:NANDgateisequivalenttotheinvertedinputOR gate 2) ANDgateisequivalenttotheinvertedinputNORgate:  ANDgateisequivalenttotheinverted inputNORgate:3) NORgateisequivalenttotheinvertedinputANDgate: NORgateisequivalenttotheinverted inputANDgate:4) ORgateisequivalenttotheinvertedinputNANDgate: ORgateisequivalenttotheinverted inputNANDgate:Example1:ImplementthefollowingSOPexpressionusingNANDgates:Y=ABC+BCD+CDEStep1:ImplementingSOPexpressionusingAND,ORGates Step2:BubblesareintroducedattheoutputoftheANDgateandattheinputoftheORgate.  BubblesattheinputandoutputStep3:BubbledinputORgateisreplacedwithNANDgate.NowallthegatesareNANDgate.  AllgatesreplacedbyNANDgateExample2:ImplementthefollowingPOSexpressionusingNORgates:Y=(A+B+C).(B+C+D).(C+D+E)Step1:ImplementationPOSexpressionusingOR,ANDgateStep2:BubblesareintroducedattheoutputoftheORgateandattheinputoftheANDgate.  BubblesintroducedintheinputandoutputStep3:BubbledinputANDgateisreplacedwithNORgate.NowallthegatesareNORgate.AllgatesreplacedbyNORGate  Tags: DigitalElectronics Minimizationtechniques Facebook Twitter Youmayliketheseposts PostaComment 0 Comments SocialPlugin Categories DigitalElectronics 19 Diodes 13 Electronicdevices 49 Minimizationtechniques 19 Poweranddisplaydevices 6 Rectifiers 4 Specialsemiconductordevices 14 Transistors 15 PopularPosts MOSFETtypes,construction,workingandCharacteristics July31,2020 CommonEmitterconfiguration,InputandOutputCharacteristics August24,2020 Solarcell,construction,working,V-IcharacteristicsandApplications November11,2020 MenuFooterWidget Home About ContactUs Privacypolicy CreatedBySoraTemplates