Basic Gates and Functions

Truth tables are used to help show the function of a logic gate. If you are unsure about truth tables and need guidence on how go about drawning them for ... BasicGatesandFunctions Introduction TruthTables LogicGates ANDgate ORgate NOTgate NANDgate NORgate EORgate ENORgate Example Problem MultipleInputGates TutorialswithLabVIEWSimulations GatesandFunctionsQuiz     Introduction Booleanfunctionsmaybepracticallyimplementedbyusingelectronicgates. Thefollowingpointsareimportanttounderstand. Electronicgatesrequireapowersupply. GateINPUTSaredrivenbyvoltageshavingtwonominal values,e.g.0Vand5Vrepresentinglogic0andlogic1respectively. TheOUTPUTofagateprovidestwonominalvaluesof voltageonly,e.g.0Vand5Vrepresentinglogic0andlogic1respectively. Ingeneral,thereisonlyoneoutputtoalogicgateexceptinsomespecial cases. Thereisalwaysatimedelaybetweenaninputbeingappliedandthe outputresponding.     TruthTables Truthtablesareusedtohelpshowthefunction ofalogicgate.Ifyouareunsureabouttruth tablesandneedguidenceonhowgoaboutdrawningthemforindividual gatesorlogiccircuitsthenusethetruthtable sectionlink. Truth Tables     Logicgates Digitalsystemsaresaidtobeconstructedbyusinglogicgates.These gatesaretheAND,OR,NOT,NAND,NOR,EXORandEXNORgates.Thebasicoperations aredescribedbelowwiththeaidoftruthtables. ANDgate TheANDgateisanelectroniccircuitthatgivesahigh output(1)onlyifallitsinputsarehigh. Adot(.)is usedtoshowtheANDoperationi.e.A.B. Bearinmindthatthis dotissometimesomittedi.e.AB   ORgate TheORgateisanelectroniccircuitthatgivesahighoutput(1)if oneormoreofitsinputsarehigh. Aplus(+) isusedtoshowtheORoperation.   NOTgate TheNOTgateisanelectroniccircuitthatproducesaninvertedversion oftheinputatitsoutput. Itisalsoknownasaninverter.  IftheinputvariableisA,theinvertedoutputisknownasNOT A. ThisisalsoshownasA',orAwithabaroverthetop,asshown attheoutputs.ThediagramsbelowshowtwowaysthattheNANDlogicgate canbeconfiguredtoproduceaNOTgate.ItcanalsobedoneusingNOR logicgatesinthesameway.   NANDgate ThisisaNOT-ANDgatewhichisequaltoanANDgatefollowedbyaNOT gate. TheoutputsofallNANDgatesarehighifanyofthe inputsarelow.ThesymbolisanANDgatewithasmallcircleontheoutput. Thesmallcirclerepresentsinversion.   NORgate ThisisaNOT-ORgatewhichisequaltoanORgatefollowedbyaNOT gate. TheoutputsofallNORgatesarelowifanyofthe inputsarehigh. ThesymbolisanORgatewithasmallcircleontheoutput.Thesmall circlerepresentsinversion.     EXORgate The'Exclusive-OR'gateisacircuitwhichwillgiveahighoutput ifeither,butnotboth,ofitstwoinputsarehigh. Anencircled plussign()isusedtoshowtheEORoperation. EXNORgate The'Exclusive-NOR'gatecircuitdoestheoppositeto theEORgate.Itwillgivealowoutputifeither,butnotboth, ofitstwoinputsarehigh.ThesymbolisanEXORgatewithasmallcircle ontheoutput.Thesmallcirclerepresentsinversion.   TheNANDandNORgatesarecalleduniversalfunctionssincewith eitheronetheANDandORfunctionsandNOTcanbegenerated. Note: AfunctioninsumofproductsformcanbeimplementedusingNAND gatesbyreplacingallANDandORgatesbyNANDgates. AfunctioninproductofsumsformcanbeimplementedusingNOR gatesbyreplacingallANDandORgatesbyNORgates. Table1:Logicgatesymbols Table2isasummarytruthtableoftheinput/outputcombinationsforthe NOTgatetogetherwithallpossibleinput/outputcombinationsfortheother gatefunctions.Alsonotethatatruthtablewith'n' inputshas2nrows.Youcancomparetheoutputsofdifferent gates. Table2:Logicgatesrepresentationusingthe Truthtable     Example ANANDgatecanbeusedasaNOT gateusingeitherofthefollowingwiringconfigurations.                                         (You cancheckthisoutusingatruthtable.)     Problem Drawthecircuitdiagramsliketheonesintheexample abovetoshowhowaNORgatecanbemadeintoaNOTgate. Clickhereforanswers.     MultipleInputGates Therearealsomultipleinputgatesifyou wanttoknowmoreaboutthemthenclickonthelinkbelow. Multiple InputGates     TutorialswithLabVIEWsimulations HerearesometutorialsusingLabVIEW simulationstoshowthegatefunctionsandsomeofthedifferentways thatgatescanbeconfigured. Tutorials andSimulations     Gates andFunctionsQuiz Thereisaquizavailabletotestwhatyou havelearnedsofar.quiz   Tosubmityourquestionsandqueriespleaseclickhere: ComposedbyWaleSangosanya   1997    UpdatedbyDavidBelton-April98 UpdatedbyRichardBigwood 2005