数字电子技术(Floyd 第十版)课件Chapter -04-stPPT格式课件下载.ppt

数字电子技术(Floyd 第十版)课件Chapter -04-stPPT格式课件下载.ppt

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,DigitalFundamentalsTenthEditionFloyd,Chapter4,2008PearsonEducation,InBooleanalgebra,avariableisasymbolusedtorepresentanaction,acondition,ordata.Asinglevariablecanonlyhaveavalueof1or0.,Summary,BooleanAddition,Thecomplementrepresentstheinverseofavariableandisindicatedwithanoverbar.Thus,thecomplementofAisA.,Aliteralisavariableoritscomplement.,AdditionisequivalenttotheORoperation.Thesumtermis1ifoneormoreiftheliteralsare1.Thesumtermiszeroonlyifeachliteralis0.,Summary,Example,Solution,Eachliteralmust=0;@#@thereforeA=1,B=0andC=1.,InBooleanalgebra,multiplicationisequivalenttotheANDoperation.Theproductofliteralsformsaproductterm.Theproducttermwillbe1onlyifalloftheliteralsare1.,Summary,BooleanMultiplication,Summary,Example,Solution,Eachliteralmust=1;@#@thereforeA=1,B=0andC=0.,Summary,CommutativeLaws,Intermsoftheresult,theorderinwhichvariablesareORedmakesnodifference.,Thecommutativelawsareappliedtoadditionandmultiplication.Foraddition,thecommutativelawstates,A+B=B+A,Intermsoftheresult,theorderinwhichvariablesareANDedmakesnodifference.,Formultiplication,thecommutativelawstates,AB=BA,Summary,AssociativeLaws,WhenORingmorethantwovariables,theresultisthesameregardlessofthegroupingofthevariables.,Theassociativelawsarealsoappliedtoadditionandmultiplication.Foraddition,theassociativelawstates,A+（B+C）=（A+B）+C,Formultiplication,theassociativelawstates,WhenANDingmorethantwovariables,theresultisthesameregardlessofthegroupingofthevariables.,A（BC）=（AB）C,Summary,DistributiveLaw,Thedistributivelawisthefactoringlaw.Acommonvariablecanbefactoredfromanexpressionjustasinordinaryalgebra.Thatis,AB+AC=A（B+C）,Thedistributivelawcanbeillustratedwithequivalentcircuits:

@#@,AB+AC,A（B+C）,Summary,RulesofBooleanAlgebra,1.A+0=A,2.A+1=1,3.A.0=0,4.A.1=1,5.A+A=A,7.A.A=A,10.A+AB=A,12.（A+B）（A+C）=A+BC,