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)

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X Y ZResult from theprevious exp

NANDimplementation

NORimplementation

000

001

010

011

100

101

110 111

Questions:

1)  ImplementaNORgateusingNANDgates,thenimplementANANDgateusingNORgates?2)  Giveasummaryofthepointsyoulearnedfromtheexperiment.