NOR and NAND Implementation – Two Level & Multilevel

MULTI-LEVEL Implementation using NAND Gate NORandNANDImplementation–TwoLevel&Multilevel TableofContents IntroductiontoNORGate&ItsImplementation NOTGateORGateANDGateOR-INVERTINVERT-ANDTwo-LevelImplementationusingNORGate ProductofSumFormMixedNotationNORGateConversionMulti-levelImplementationusingNORGate 3-LevelImplementation&ExampleusingNORGateIntroductiontoNANDGate&ItsImplementation NOTGATEANDGATEORGATEAND-INVERTINVERT-ORTwo-LevelImplementationusingNANDGate SumofProductFormMixedNotationNANDGateConversion&Example MULTI-LEVELImplementationusingNANDGate Three-levelImplementation&ExampleusingNANDGate IntroductiontoNORGate&ItsImplementation NORgateisauniversalgatewhichcanimplementanykindofBooleanlogicfunction. NORgateiscommerciallyusedbecauseitallowstheaccesstowiredlogic,whichisalogicfunctionformedbyconnectingtheoutputsofNORgates.Wiredlogicdoesnotconsistofaphysicalgatebutthewiresbehaveasalogicfunction.TheotherreasonforcommercialusageofNORgateisthatitcanbeeasilyfabricatedandhasalowfabricationcost.Italsoshrinkstheschematicbydecreasingthenumberofgates,whichresultsinsmallsize,fastspeed,andLowpowerconsumption. AsweknowatypicalBooleanfunctionimplementationconsistsofANDGate,ORGateandNOTGate.ToimplementawholeBooleanfunctionusingNORgatefirst,weneedtoimplementthesegatesusingNORgates. RelatedArticle:Exclusive-NOR(XNOR)DigitalLogicGate NOTGate NOTorInvertergatecomplementsitsinputintooutput.AsingleinputNORgatealsoinvertsitsinput.SingleinputNORgatemeansthatitsinputsarecombinedintosingleinputlineasshowninthefiguregivenbelow. ORGate ORlogicgatefunctioniscomplement(Invert)ofNORfunction.SoinordertoimplementORgateweneedtwoNORgates.ThesecondNORgatewillbeusedforcomplementingtheoutputofthefirstNORgate.SchematicofORgateusingNANDgateisgivenbelow. ANDGate ToacquireANDlogicgateoperationweneedthreeNORgates.TwoNORgateareusedasInvertertoinverttheinputtothe3rdNORgate. AccordingtoDeMorgan’slaw (A’+B’) = A.B SchematicofANDgateimplementationusingNORgateisgivenbelow. ToconvertaBooleancircuitwithAND,ORandNOTgatesintoNORgates,weneedtoconvertthelogicfunctionschematicintoNORequivalentschematic.ANORequivalentschematiccontainsNORequivalentgatesforeverylogicgate.Thesegatesneedalternatelogicsymbols.WewilldiscussthesealternateNORgatesonebyone. OR-INVERT OR-INVERTsymbolconsistsofORgatesymbolwithabubbleattheoutput,whichcomplementstheoutputofORintoNOR. INVERT-AND INVERT-ANDmeanINVERTERconnectedtotheinputofANDgate.AccordingtoDEMorgan’slaw,InvertingtheinputsoftheANDgateconvertitintoNORgate. (A’.B’.C’)  =  (A+B+C)’ INVERT-ANDsymbolisgivenbelow. INVERT-ANDsymbolconsistsofANDgatewithabubbleateachinputforcomplementation(inversion).  ThesesymbolsareusedforconvertingacircuitintoNORgates.Whenbothofthesesymbolsareusedinaschematic,itissaidtobeinmixednotation. RelatedArticles DigitalFlip-Flops–SR,D,JKandTFlipFlops DigitalLatches–TypesofLatches–SR&DLatches Two-LevelImplementationusingNORGate Two-levelimplementationmeansthatanypathfrominputtooutputcontainsmaximumtwogateshencethenametwo-levelforthetwolevelsofgates. ImplementingTwo-LevellogicusingNORgaterequirestheBooleanexpressiontobeinProductofSum(POS)form. InProductofSumform,1stlevelofthegateisORgateand2ndlevelofthegateisANDgate. ToimplementaBooleanfunctionusingNORgate,therearebasicallythreestep; ProductofSumForm First,youneedtohaveasimplifiedProductofSumexpressionforthefunctionyouneedtoimplement. SimplifiedProductofSumexpressioncanbemadeusingKarnaughMap(K-map)bycombiningthe‘0’sandtheninvertingtheoutputfunction. SupposewehavesimplifiedPOSexpression. F = (A+B)(C+D) DrawitsschematicusingAND-ORNOTgatesasshowninthefiguregivenbelow. MixedNotation Nextstepistodrawtheabove-mentionedschematicusingOR-InvertandInvert-ANDgates.OR-InvertshouldreplaceORgatesandinvert-ANDreplacesANDgates.Thisschematicissaidtobeinmixednotationanditsschematicisgivenbelow. Abubblemeanscomplement.Twobubblesalongalinemeandoublecomplementationandtheycanceleachother.However,asinglebubblealongalineshouldbecompensatedbyinsertinganInverterinthatlineorifitisaninputlinethenyoucanalsofeedacomplementedinputifavailable. RelatedPost: BinaryEncoder–Construction,Types&Applications BinaryDecoder–Construction,Types&Applications NORGateConversion ThelaststepistoredrawthewholeschematicreplacingOR-InvertandInvert-ANDgatesymbolbyNORgatesymbolbecauseOR-InvertandInvert-ANDareequivalenttoNORgate.Thefinalschematicisshowninthefiguregivenbelow. Exampleofhavingsinglebubbleinaline: F = (A+B)(B+C)D ThisfunctionisinsimplifiedProductofSumform.First,weneedtodrawitsOR-ANDschematic. Nowweconverttheabove-givenschematicintomixednotationbyconvertingORgateintoOR-INVERTandANDgateintoINVERT-AND. InputlineDtotheinputofANDgatehasasinglebubble.TocompensatethisbubbleweneedtoeitherinsertaninverterinthislineorcomplementtheinputDifavailable. NowreplaceeveryOR-InvertandInvert-ANDwithNORgateasshowninthefiguregivenbelow. Multi-levelImplementationusingNORGate Schematichavingmorethantwolevelsofgatesisknownasamulti-levelschematic. Wecanimplementmulti-levelPOSexpressionusingNORgate.Theconversionofmulti-levelexpressionintoNORgatehasthesamemethodastwo-levelimplementation. Themulti-levelexpressioncanbeconvertedintotwo-levelexpressionbutforthesakeofrealization,wewillimplementamulti-levelexpression. Supposea4-levelfunction: F = (A+B(C+D))(B+D’) First,wewilldrawitsschematicusingAND,OR,NOTgates. NoticetheOR-ANDpatternliketwo-levelimplementation.Itcanbeeasilyconvertedsincethebubblecancelseachother. NowwewillconvertitintomixednotationforNOR. Thetwobubblesalongasinglelinecanceleachother.However,thereisasinglebubbleatthe2ndlevelgate’sinput.sowewillcomplementtheinputBtocompensatethebubble. NowredrawthewholeschematicreplacingOR-InvertandInvert-ANDwithNORgatesymbolasshowninthefigurebelow. 3-LevelImplementation&ExampleusingNORGate A3-levelimplementationusingNORgate’sExampleisgivenbelow; F = (AB’+CD’)(A’+B) First,wewilldrawitsschematicusingAND,OR,NOTgatesasgiveninthefigurebelow. NowwewillconvertitintomixednotationforNOR. Thesinglebubblesattheinputlineofallfirstlevelgatesneedaninverterortheinputstobecomplimented.Thetwobubblesalongthesamelinecanceleachother. Nowthatallthebubbleshavebeenaccountedfor,wewillredrawthisschematicbyreplacingOR-InvertandInvert-ANDwithNORgatesasshowninthefigurebelow. IntroductiontoNANDGate&ItsImplementation NANDGateisauniversallogicgatewhichmeansanyBooleanlogiccanbeimplementedusingNANDgateincludingindividuallogicgates.Inotherwords,anykindofBooleanfunctioncanbeimplementedusingonlyNANDgates. NANDgateiscommerciallyusedbecauseitallowstheaccesstowiredlogicwhichisalogicfunctionformedbyconnectingtheoutputsofNANDgates.Wiredlogicdoesnotconsistofaphysicalgatebutthewiresbehaveasalogicfunction.TheotherreasonforcommercialusageofNANDgateisthatitcanbeeasilyfabricatedandhasalowfabricationcost.Italsoshrinkstheschematicbydecreasingthenumberofgates,whichresultsinsmallsizeandasmalldelay,fastspeedandLowpowerconsumption. AsweknowatypicalBooleanfunctionimplementationconsistsofAND,ORandNOTgates.ToimplementawholeBooleanfunctionusingNANDgatefirst,weneedtoconvertthesegatesintoNANDgate. RelatedArticles: DigitalAsynchronousCounter(RippleCounter)–Types,Working&Application DigitalSynchronousCounter–Types,Working&Applications NOTGATE NOTgate(Inverter)complementsitsinputintotheoutput.AsingleinputNANDgatealsocomplementsitinputintooutput.SingleinputNANDgatemeansthattheinputsof2-inputNANDgatesarecombinedtogetherintoasingleinputlineasshowninthefiguregivenbelow. ANDGATE NANDgateisnegativeANDgate.Infact,NANDandANDareinversetoeachother.ToachieveANDgateoperationneedtwoNANDgates.ThesecondNANDgatewillbeusedasanInvertertocomplement(Invert)theoutputoffirstNANDgateintoANDgate. ORGATE ORgateoperationneedsthreeNANDgates.TwoNANDgatesareusedasinverterattheinputofthe3rdNANDgate.ThetwoNANDgatesinverttheinputandthentheinvertedinputisfedtothe3rdNANDgate,whichresultsinORfunctionasshowninfigurebelow; (A’.B’) =            A+B       DEMorgan’slaw ToconvertaBooleanfunctionfromNOT,AND,ORgatestoNANDgates,weneedtoconverttheschematicintoNANDequivalentschematic.NANDequivalentschematiccontainsNANDequivalentgates.Theseequivalentgatesneedalternativesymbolstorepresent;thesealternativegatesarediscussedbelow; BCDto7-SegmentDisplayDecoder–Construction,Circuit&Operation BinaryMultiplier–Types&BinaryMultiplicationCalculator AND-INVERT AND-INVERTmeansINVERTER(NOTgate)connectedtotheoutputofANDgate.AswehavediscussedbeforethatinvertingtheoutputofanANDgatemakesitaNANDgate.AND-INVERTsymbolrepresentNANDgateanditisgivenbelow; AND-INVERTsymbolconsistsofANDgatefollowedbysmallbubbleforcomplementingtheoutput. INVERT-OR INVERT-ORmeansInverter(NOTgate)connectedtotheinputofORgate.AccordingtoDEMorgan’slaw,InvertingtheinputstotheORgatemakesitaNANDgate.SoINVERT-ORsymbolrepresentsNANDgateanditisgiveninthefigurebelow. INVERT-ORsymbolconsistsofORgatewithsmallcircles(bubble)attheinputforinversion. ThesebothsymbolsareusedforconvertingaschematicintoNANDgates.Whenbothofthesesymbolsareusedinaschematicthecircuitisknowntobeinmixednotation. RelatedArticles: MUX–DigitalMultiplexer|Types,Construction&Applications DEMUX–Demultiplexer|Types,Construction&Applications Two-LevelImplementationusingNANDGate Two-levelimplementationmeansthatanypathfrominputtooutputcontainsmaximumtwogateshencethenametwo-levelforthetwolevelsofgates. Implementingatwo-levelschematicwithNANDgatesrequiretheexpressiontobeinSumofProduct(SOP)form.InSumofProductform,the1stlevelofthegateisANDgateandthe2ndlevelofthegateisORgate.ItcanbeeasilyconvertedintoNANDgates.Toconvertanyfunctionintotwo-levelNANDschematicthereare3steps; SumofProductForm First,youneedtohavesimplifiedSumofProduct(SOP)formfortheBooleanfunction.Karnaughmap(K-map)orBooleanalgebraictheoremscanbeusedtogetaSimplifiedSOPexpression. SupposeanSOPfunctionF=AB+CD ThisSOPfunctionisinSimplifiedSOPformanditsAND-ORschematicisgivenbelow. MixedNotation 2ndstepistoconverttheAND-ORschematicintomixednotation.InmixednotationforNANDgate,ANDgateisconvertedintoAND-invertandORgateisconvertedintoINVERT-OR.Mixednotationdesignfortheabovefunctionisgivenbelow. Noticethebubbleinasingleline.Asinglebubblemeansacomplement(inversion).Twobubblesonthesamelinemeandoublecomplementationwhichcancelseachother.Iftherewasasinglebubbleonalinethenwehavetoinsertaninverterinthatline.Wewilldiscussthatinanotherexample. Alsoread: ComparatorandDigitalMagnitudeComparator 555Timer NANDGateConversion&Example ThethirdstepistoconverttheAND-INVERTandINVERT-ORsymbolsintoitsequivalentNANDgatesymbol.NANDgateschematicofabovefunctionisgivenbelow. Example SupposeafunctionF=AB+BC+DtobeimplementedusingNANDgates ThisfunctionisinsimplifiedSumofProductform.First,weneedtodrawitsAND-ORschematic. Nowweconverttheabove-givenschematicintomixednotationbyconvertingANDgateintoAND-INVERTandORgateintoINVERT-OR. NoticethesingleinputDlinetotheORgate.Thereisonebubbleonthisline.TocompensatethisbubbleweneedtoeitherinsertaninverterinthislineorcomplementtheinputDifavailable.ThenconvertAND-INVERTandINVERT-ORsymbolintoNANDsymbolasshowninthefiguregivenbelow; TheinverterusedhereisalsoasingleinputNANDgate. RelatedPosts: Half&FullAdder&Subtractor RippleCarryAndCarryLookAheadAdder MULTI-LEVELImplementationusingNANDGate Schematichavingmorethantwolevelsofgatesisknownasamulti-levelschematic. Wecanimplementmulti-levelSOPexpressionusingNANDgate.Theconversionofmulti-levelexpressionintoNANDgatehasthesamemethodastwo-levelimplementation. Themulti-levelexpressioncanbeconvertedintotwo-levelexpressionbutforthesakeofrealization,wewillimplementamulti-levelexpression. Supposeamulti-levelfunctionbe;                                                F=A(B+CD)+BD’ Thisisafour-levelfunction First,wewilldrawitsAND-ORschematic NoticetheAND-ORpattern.SoitcanbeeasilyconvertedintoNANDgates.Nowwewillconvertthisintomixednotationi.e.ANDgatewillbeconvertedintoAND-INVERTandORwillbeconvertedintoINVERT-ORasshowninthefiguregivenbelow. Rememberdoublebubblesalongasinglelinecanceleachother,andasinglebubblealongalineshouldbecompensatedbyinsertinganinverterinthatline. Noticethe3rdlineofinputB,thereisasinglebubble.Tocompensatethisbubble,eitheraninvertershouldbeaddedortheinputBshouldbecomplimented. ThenredrawthewholeschematicusingallNANDgatesbyreplacingAND-INVERTandINVERT-ORwithNANDgatesasshowninthefigurebelow. Three-levelImplementation&ExampleusingNANDGate Suppose3-levelfunctionbe      F=(AB’+CD’)(A’+B) First,wewilldrawitsAND-ORschematicasshowninthefigurebelow; ThenwewillconvertitintoMixednotationbyconvertingANDintoAND-INVERTandORintoINVERT-OR. Noticethelasttwolineswithsinglebubbles.Thesesinglebubblesshouldbecompensatedbyinsertinginvertersinthoselinesorcomplementingtheinputs.Theoutputalsocontainsasinglebubblesoaninverterattheoutputshouldalsobeconnectedtocompensatethebubble. AndthelaststepistoredrawthewholeschematicusingallNANDgatesinsteadofAND-INVERTandINVERT-ORasshowninthefiguregivenbelow. RelatedPosts: CounterandTypesofElectronicCounters RingCounter&JohnsonCounter–Construction&Operation Tags3-LevelImplementationNORGateMulti-levelNORGateImplementationNANDImplementationNORImplementationTwo-LevelImplementationNORGate ElectricalTechnology010minutesread ShowFullArticle Facebook Twitter LinkedIn Tumblr Pinterest Reddit VKontakte Skype Messenger Messenger WhatsApp Telegram ShareviaEmail Print ElectricalTechnology AllaboutElectrical&ElectronicsEngineering&Technology.Follow ElectricalTechnologyonFacebook,Twitter,Instagram,Pinterest,YouTube,&LinkedintogetthelatestupdatesorsubscribeHeretogetlatestEngineeringArticlesinyourmailbox. Website Facebook Twitter LinkedIn Flickr YouTube Pinterest Instagram DigitalLatches-TypesofLatches-SR&DLatches HowtoTestaDiodeusingDigital&AnalogMultimeter-4Ways. 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