Tutorial:2of10
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GORESET
TheLogic"AND"Gate
Definition
ALogicANDGateisatypeofdigitallogicgatethathasanoutputwhichisnormallyatlogiclevel"0"andonlygoes
"HIGH"toalogiclevel"1"whenALLofitsinputsareatlogiclevel"1".Theoutputstateofa"LogicANDGate"onlyreturns
"LOW"againwhenANYofitsinputsareatalogiclevel"0".InotherwordsforalogicANDgate,anyLOWinputwillgivea
LOWoutput.
ThelogicorBooleanexpressiongivenforalogicANDgateisthatforLogicalMultiplicationwhichisdenotedbyasingle
dotorfullstopsymbol,(.)givingustheBooleanexpressionof:A.B=Q.
Thenwecandefinetheoperationofa2-inputlogicANDgateasbeing:
"IfbothAandBaretrue,thenQistrue"
2-inputTransistorANDGate
Asimple2-inputlogicANDgatecanbeconstructedusingRTLResistor-transistorswitchesconnectedtogetheras
shownbelowwiththeinputsconnecteddirectlytothetransistorbases.Bothtransistorsmustbesaturated"ON"foran
outputatQ.
LogicANDGatesareavailableusingdigitalcircuitstoproducethedesiredlogicalfunctionandisgivenasymbolwhose
shaperepresentsthelogicaloperationoftheANDgate.
TheDigitalLogic"AND"Gate
2-inputANDGate
SymbolTruthTable
BAQ
000
010
100
2-inputANDGate111
BooleanExpressionQ=A.BReadasAANDBgivesQ
3-inputANDGate
SymbolTruthTable
3-inputANDGate
CBAQ
0000
0010
0100
0110
1000
1010
1100
1111
BooleanExpressionQ=A.B.CReadasAANDBANDCgivesQ
BecausetheBooleanexpressionforthelogicANDfunctionisdefinedas(.),whichisabinaryoperation,ANDgatescan
becascadedtogethertoformanynumberofindividualinputs.However,commercialavailableANDgateIC''sareonly
availableinstandard2,3,or4-inputpackages.Ifadditionalinputsarerequired,thenstandardANDgateswillneedtobe
cascadedtogethertoobtaintherequiredinputvalue,forexample.
Multi-inputANDGate
TheBooleanExpressionforthis6-inputANDgatewillthereforebe:Q=(A.B).(C.D).(E.F)
Ifthenumberofinputsrequiredisanoddnumberofinputsany"unused"inputscanbeheldHIGHbyconnectingthem
directlytothepowersupplyusingsuitable"Pull-up"resistors.
CommonlyavailabledigitallogicANDgateIC''sinclude:
TTLLogicTypes
74LS08Quad2-input
74LS11Triple3-input
74LS21Dual4-input
CMOSLogicTypes
CD4081Quad2-input
CD4073Triple3-input
CD4082Dual4-input
Quad2-inputANDGate7408
InthenexttutorialaboutDigitalLogicGates,wewilllookatthedigitallogicORGatefunctionasusedinbothTTLand
CMOSlogiccircuitsaswellasitsBooleanAlgebradefinitionandtruthtables.
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