Karnaugh map卡諾圖- DavidTsai - Google Sites
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卡諾圖是貝爾實驗室的電信工程師,莫里斯·卡諾在1953年發明的。
The Karnaugh map, also known as the K-map, is a method to simplify boolean algebra expressions.
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Karnaughmap卡諾圖
卡諾圖是真值表的變形,它可以將有n個變數的邏輯函數的個最小項組織在給定的長方形表格中,同時為相鄰最小項(相鄰與項)運用鄰接律化簡提供了直觀的圖形工具。
但是,如果需要處理的邏輯函數的自變數較多,那麼卡諾圖的行列數將迅速增加,使圖形更加複雜;此外,卡諾圖的圖形化表示方法不適合直接用於演算法的設計,因此計算機輔助工程工具一般不會使用卡諾圖來進行邏輯函數的優化。
卡諾圖是貝爾實驗室的電信工程師,莫里斯·卡諾在1953年發明的。
The Karnaughmap, alsoknownasthe K-map,isamethodtosimplify booleanalgebra expressions. MauriceKarnaugh introduceditin1953asarefinementof EdwardVeitch's1952 Veitchdiagram.TheKarnaughmapreducestheneedforextensivecalculationsbytakingadvantageofhumans'pattern-recognitioncapability.Italsopermitstherapididentificationandeliminationofpotential raceconditions.Therequiredbooleanresultsaretransferredfroma truthtable ontoatwo-dimensionalgridwherethecellsareorderedin Graycode,andeachcellrepresentsonecombinationofinputconditions.Optimalgroupsof1sor0sareidentified,whichrepresentthetermsofacanonicalform ofthelogicintheoriginaltruthtable. Thesetermscanbeusedtowriteaminimalbooleanexpressionrepresentingtherequiredlogic.Karnaughmapsareusedtosimplifyreal-worldlogicrequirementssothattheycanbeimplementedusingaminimumnumberofphysicallogicgates.A sum-of-productsexpression canalwaysbeimplementedusing ANDgates feedingintoan ORgate,anda product-of-sumsexpression leadstoORgatesfeedinganANDgate. Karnaughmapscanalsobeusedtosimplifylogicexpressionsinsoftwaredesign.Booleanconditions,asusedforexamplein conditionalstatements,cangetverycomplicated,whichmakesthecodedifficulttoreadandtomaintain.Onceminimised,canonicalsum-of-productsandproduct-of-sumsexpressionscanbeimplementeddirectlyusingANDandORlogicoperators.YouTube影片
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