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1、2021/9/1Chapter4BooleanAlgebraandLogicSimplification1Chapter4OutlineLecture6:BooleanAlgebra4-1BooleanOperationsandExpressions4-2LawsandRulesofBooleanAlgebra4-3DeMorgan’sTheorems4-4BooleanAnalysisofLogicCircuits4-5SimplificationUsingBooleanAlgebra4-6Standard
2、FormsofBooleanExpressions4-7BooleanExpressionsandTruthTables4-8TheKarnaughMap4-9KarnaughMapSOPMinimization4-10KarnaughMapPOSMinimization***DigitalSystemApplicationLecture6Lecture72021/9/1Chapter4BooleanAlgebraandLogicSimplification2KeyKnowledgeinLecture6Lec
3、ture6:BooleanAlgebraTwoformsoflogicexpression:SOPandPOSform.Conceptofmaxtermandminterm;Evaluateasumterm(maxterm)andaproductterm(minterm).ThreebasiclawsandtwelveoperationrulesandthreefundamentalrulesofBooleanalgebra.ApplyingDeMorgan’sTheorem.Logicexpressions
4、implificationusingBooleanalgebra.Booleananalysisoflogiccircuits.DifficultTopics:ConvertingbetweenSOPandPOSexpression.Logicexpressionsimplification.2021/9/1Chapter4BooleanAlgebraandLogicSimplification3BooleanOperationsandExpressionsLecture6:BooleanAlgebraCon
5、ceptofvariable,complement,andliteralAvariableisasymbolusedtorepresentalogicquantity.Itcanhavea1ora0value.Thecomplementistheinverseofavariableandisindicatedbyabaroverthevariable(overbar).Aliteralisavariableorthecomplementofavariable.2021/9/1Chapter4BooleanAl
6、gebraandLogicSimplification4BooleanOperationsandExpressionsLecture6:BooleanAlgebraAddition0+0=00+1=11+0=11+1=1Multiplication0*0=00*1=01*0=01*1=1ORGateANDGate2021/9/1Chapter4BooleanAlgebraandLogicSimplification5EvaluatelogicexpressionLecture6:BooleanAlgebraD
7、eterminethevaluesA,B,C,andDthatmakethesumtermSolution:forthesumtermtobe0,eachoftheliteralsinthetermmustbe0.Therefore,A=0,B=1,C=0,andD=1.DeterminethevaluesA,B,C,andDthatmaketheproducttermSolution:fortheproducttermtobe1,eachoftheliteralsinthetermmustbe1.There
8、fore,A=1,B=0,C=1,andD=0.2021/9/1Chapter4BooleanAlgebraandLogicSimplification6LawsofBooleanAlgebraLecture6:BooleanAlgebraThebasiclawsofBooleanalgebraare:CommutativeLaws(交换律)AssociativeLaws(结合律)Distribut
