电子专业参赛课件 数字电子技术(课件)lec07

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1、2021/7/3Chapter4BooleanAlgebraandLogicSimplification1Lecture7OutlineLecture7:LogicSimplificationUsingK-map4-7BooleanExpressionsandTruthTables4-8TheKarnaughMap4-9KarnaughMapSOPMinimization4-10KarnaughMapPOSMinimization2021/7/3Chapter4BooleanAlgebraandLogicSimp

2、lification2KeyKnowledgeinLecture7Lecture7:LogicSimplificationUsingK-mapTruthtableandBooleanexpressionconversionThestructureofKarnaughmap.ConstructKarnaughmapfromdifferentsources.UseKarnaughmaptosimplifylogicexpressions.Makeuseofdon’tcareconditionsinK-map.Conv

3、ersionbetweenSOPandPOSusingK-map.Sevensegmentdisplaydecoderworkingprinciple.DifficultTopics:GettoknowK-mapandtheconstructionofK-map;ConversionbetweenSOPandPOSusingK-map;7-segmentdisplaydecoder.2021/7/3Chapter4BooleanAlgebraandLogicSimplification311111BooleanE

4、xpressionsandTruthTablesLecture7:LogicSimplificationUsingK-mapDevelopatruthtableforthestandardSOPexpression.Solution:1.Listeightcombinationsofbinaryvalues;2.Determinemintermbinaryvalues;3.Placea1intheXcolumncorrespondingtotheabovebinaryvaluesand0elsewhere0000

5、0INPUTSABCOUTPUTXPRODUCTTERM0000010100111001011101112021/7/3Chapter4BooleanAlgebraandLogicSimplification400000ConvertingPOSExpressionstoTruthTableFormatLecture7:LogicSimplificationUsingK-mapDevelopatruthtableforthestandardPOSexpression.Solution:1.Listeightcom

6、binationsofbinaryvalues;2.Determinemaxtermbinaryvalues;3.Placea0intheXcolumncorrespondingtotheabovebinaryvaluesand1elsewhere.111INPUTSABCOUTPUTXSUMTERM0000010100111001011101112021/7/3Chapter4BooleanAlgebraandLogicSimplification5DetermineStandardExpressionsfro

7、maTruthTableLecture7:LogicSimplificationUsingK-mapFromthegiventruthtable,determinethestandardSOPexpressionandtheequivalentstandardPOSexpression.INPUTSABCOUTPUTX000001010011100101110111000110111.FortheSOPexpressionConvertbinaryvaluesthatmakeoutputequal1toprodu

8、ctterms.TheresultingSOPexpressionis:2.ForthePOSexpressionConvertbinaryvaluesthatmakeoutputequal0tosumterms.TheresultingPOS:2021/7/3Chapter4BooleanAlgebraandLogicSimplification6TheKarnaugh