数字电子技术(课件)lec07

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1、2021/6/13Chapter4BooleanAlgebraandLogicSimplification1Lecture7OutlineLecture7:LogicSimplificationUsingK-map4-7BooleanExpressionsandTruthTables4-8TheKarnaughMap4-9KarnaughMapSOPMinimization4-10KarnaughMapPOSMinimization2021/6/13Chapter4BooleanAlgebraandLogicSimplification2Ke

2、yKnowledgeinLecture7Lecture7:LogicSimplificationUsingK-mapTruthtableandBooleanexpressionconversionThestructureofKarnaughmap.ConstructKarnaughmapfromdifferentsources.UseKarnaughmaptosimplifylogicexpressions.Makeuseofdon’tcareconditionsinK-map.ConversionbetweenSOPandPOSusingK

3、-map.Sevensegmentdisplaydecoderworkingprinciple.DifficultTopics:GettoknowK-mapandtheconstructionofK-map;ConversionbetweenSOPandPOSusingK-map;7-segmentdisplaydecoder.2021/6/13Chapter4BooleanAlgebraandLogicSimplification311111BooleanExpressionsandTruthTablesLecture7:LogicSimp

4、lificationUsingK-mapDevelopatruthtableforthestandardSOPexpression.Solution:1.Listeightcombinationsofbinaryvalues;2.Determinemintermbinaryvalues;3.Placea1intheXcolumncorrespondingtotheabovebinaryvaluesand0elsewhere00000INPUTSABCOUTPUTXPRODUCTTERM0000010100111001011101112021/

5、6/13Chapter4BooleanAlgebraandLogicSimplification400000ConvertingPOSExpressionstoTruthTableFormatLecture7:LogicSimplificationUsingK-mapDevelopatruthtableforthestandardPOSexpression.Solution:1.Listeightcombinationsofbinaryvalues;2.Determinemaxtermbinaryvalues;3.Placea0intheXc

6、olumncorrespondingtotheabovebinaryvaluesand1elsewhere.111INPUTSABCOUTPUTXSUMTERM0000010100111001011101112021/6/13Chapter4BooleanAlgebraandLogicSimplification5DetermineStandardExpressionsfromaTruthTableLecture7:LogicSimplificationUsingK-mapFromthegiventruthtable,determinethe

7、standardSOPexpressionandtheequivalentstandardPOSexpression.INPUTSABCOUTPUTX000001010011100101110111000110111.FortheSOPexpressionConvertbinaryvaluesthatmakeoutputequal1toproductterms.TheresultingSOPexpressionis:2.ForthePOSexpressionConvertbinaryvaluesthatmakeoutputequal0tosu

8、mterms.TheresultingPOS:2021/6/13Chapter4BooleanAlgebraandLogicSimplification6TheKa