all gates using universal gates

Experiment 3) NAND & NOR Implementation 5.1 Objectives: • Todemonstratethe implementatio nofadigitalsystemsingNANDand NORgates. 5.2 Background Information : NAND an d NOR ga tes is sa id to be un iver sa l gates be cause any di gi tal syst em can be implementedusingonlyoneofthesegates. Digi talcircui tsarefrequent lyconstru ctedwithonlyNANDorNORgates;becau sethesegatesare easiertofabricatewithelectronic components.Becauseoftheimpo rtanceofNANDandNORinthe desi gn of di gi tal circuits, rules and pr ocedures have been develope d for the conver si on fr om Boo lea n fun cti ons in terms of AND, OR and NOT into equ iva len t NAN D orNOR log icdiagr ams. NANDandNORarecalleduniversalgatesbecauseanydigitalsystemorBooleanfunctioncanbe implementedwithonlythesegates. FromDeMorga ntheorem,wecan seeotherrepres entationforNAND andNORgatesa sfollows: TwosymbolsforNAND TwosymbolsforNOR 5.3 Equipment Requires : Thefollowing equipmentsare neededtoperformalltheprocedure s: UniversalBreadboard Jumperwirekit (1)7400TTL QUAD2-INPUTNAND GATE (1)7402TTL QUAD2-INPUTNOR GATE (1)7410TTL TRIPLE3-INPUTNAND GATE (1)7427TTL TRIPLE3-INPUTNOR GATE 2xToggleSwitches 1xCarbon-filmResistor(470 Ω) 1xLED 5.4 Procedure : 1.UsingonlyNAND andNORgatestoimplementallbasi clogicgatesandthe nverifyyourresults.

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7/22/2019 All Gates Using Universal Gates

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Experiment 3)

NAND & NOR Implementation

5.1 Objectives:

• TodemonstratetheimplementationofadigitalsystemsingNANDandNORgates.

5.2 Background Information :NAND and NOR gates is said to be universal gates because any digital system can beimplementedusingonlyoneofthesegates.

DigitalcircuitsarefrequentlyconstructedwithonlyNANDorNORgates;becausethesegatesareeasiertofabricatewithelectroniccomponents.BecauseoftheimportanceofNANDandNORinthedesign of digital circuits, rules and procedures have been developed for the conversion fromBoolean functions intermsofAND,ORandNOT intoequivalentNANDorNOR logicdiagrams.NANDandNORarecalleduniversalgatesbecauseanydigitalsystemorBooleanfunctioncanbeimplementedwithonlythesegates.

FromDeMorgantheorem,wecanseeotherrepresentationforNANDandNORgatesasfollows:

TwosymbolsforNAND

TwosymbolsforNOR

5.3 Equipment Requires :

Thefollowingequipmentsareneededtoperformalltheprocedures:

UniversalBreadboardJumperwirekit

(1)7400TTLQUAD2-INPUTNANDGATE

(1)7402TTLQUAD2-INPUTNORGATE

(1)7410TTLTRIPLE3-INPUTNANDGATE

(1)7427TTLTRIPLE3-INPUTNORGATE

2xToggleSwitches1xCarbon-filmResistor(470Ω)

1xLED

5.4 Procedure :

1.UsingonlyNANDandNORgatestoimplementallbasiclogicgatesandthenverifyyourresults.

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ImplementationofAND,OR,NOTusingNAND

ImplementationofAND,OR,NOTusingNOR

2.NANDImplementationofBooleanfunctions:

Assumethatallvariablesandtheircomplementsareavailableasinputs. FindtheminimumSOPexpressionofthefunction. Drawthecorrespondingtwo-levelAND-ORcircuitdiagram. ReplaceallgateswithNANDgates;learningthegatesinterconnectionsarekeptunchanged.

Example:

TrytoimplementthefunctionF,fromthepreviousexperiment,usingonlyNANDgates,andthenverifyyourresults.

F=x’y’z+x’yz+xy’

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3.NORImplementationofBooleanfunctions:

Assumethatallvariablesandtheircomplementsareavailableasinputs. FindtheminimumPOSexpressionofthefunction. Drawthecorrespondingtwo-levelOR-ANDcircuitdiagram. ReplaceallgateswithNORgates,learningthegatesinterconnectionsarekeptunchanged.Example:

TrytoimplementthesamefunctionF,usingonlyNORgates,thenverifyyourresults.

F=x’y’z+x’yz+xy’

F’=(x’y’z+x’yz+xy’)’

F’=(x’y’z)’(x’yz)’(xy’)’

F’=(x+y+z’)(x+y’+z’)(x’+y)