第3章(2學(xué)時) 組合線路的邏輯設(shè)計-英文

ComputerOrganizationChapter3LogicdesignofcombinationalcircuitsChapter3Logicdesignofcombinationalcircuits3.1Combinationallogicfunctionsandexpressions3.2Karnaughmapsforsimplificationoflogicfunction3.3Implementationofcombinationallogicfunctions3.4MSIcombinationalcircuitsmodel3.5SummaryBooleanalgebraandlogicexpressionAlgebraofbinaryvariablesandfunctions,namedaftera19th-centurymathematicianGeorgeBoole.Logicexpressionisanalgebraicexpressioncomposedofliteralsofindependentvariablesandlogicoperatorsactingontheseliterals.Alllogicfunctionscanberepresentedasthefunctionalcompositionsofthesethreelogicoperations（AND,OR,NOT)Usingthetruthtableisthesimplestandaccuratemethodofdefiningalogicfunction.3.1CombinationallogicfunctionsandexpressionsPrimitivecombinationalfunctionsandbasiclogicoperationsANDLogicF=A·B=A∧B=AB3.1CombinationallogicfunctionsandexpressionsABFAB00011011F0001

truthtablePrimitivecombinationalfunctionsandbasiclogicoperationsORLogicF=A＋B=A∨B=A/B3.1CombinationallogicfunctionsandexpressionsABF+AB00011011F0111truthtablePrimitivecombinationalfunctionsandbasiclogicoperationsNOTLogic F=A3.1CombinationallogicfunctionsandexpressionsAF1AFA01F10truthtablePrimitivecombinationalfunctionsandbasiclogicoperationsXORLogicF=ABXNORLogicF=A

BNADNLogicF=A·B○＋○＋3.1CombinationallogicfunctionsandexpressionsPrimitivecombinationalfunctionsandbasiclogicoperationsNORLogicF=A＋BExtendtologicfunctionsofmultiplyvariables

F=A·B·C=ABC F=A＋B＋CCombination3.1CombinationallogicfunctionsandexpressionsBooleanalgebraandlogicexpression3.1CombinationallogicfunctionsandexpressionsCombinationallogicfunction:DependentvariableisthefunctionofmerelyitsindependentvariableswithouttheinvolvementofatimevariableThereisnomemoryunit,soallthecomponentsrespondtotheinputsignalsinstantaneously.Thecurrentoutputsisdeterminedsolelybythecurrentinputs3.1CombinationallogicfunctionsandexpressionsCombinationalcircuit……inputsoutputSequentiallogicfunction:Musthaveanargumentoftimeinvolvedasanindependentvariabletoreflectthefunctionhistory.Memoryisnecessaryelementwhich“memorizes"thehistoryofthecircuit.3.1CombinationallogicfunctionsandexpressionsCombinationalcircuit……memory…………inputsoutputCurrentstatesNextstatesclock3.1CombinationallogicfunctionsandexpressionsUsingtruthtabletodefineacombinationallogicfunctionalogiccircuitfordetectingTrafficlights‘Workingstatus’Normalstate

Faultstate

3.1CombinationallogicfunctionsandexpressionsUsingtruthtabletodefineacombinationallogicfunction

InputOutputLRYG00010010010101101000101111011111枚舉出輸入的所有情況并根據(jù)事實邏輯對應(yīng)列出輸出結(jié)果此表唯一3.1CombinationallogicfunctionsandexpressionsCanonicallogicexpression(正則邏輯表達式)Therepresentationofalogicfunctionisunique,thenthesamefunctioncanberepresentedinmanydifferentBooleanexpression.ex：AB＋ABCD(E＋F)＝ABCanonicalexpressionsareintroducedandusedinthedesignmethodologyoflogiccircuits.Sumofproducts(SOP：積之和)Productofsums(POS：和之積)3.1CombinationallogicfunctionsandexpressionsUsinglogicFunction

tabletodefineacombinationallogicfunction

InputOutputLRYGm00001m10010m20101m30110m41000m51011m61101m71111L=R’Y’G’+R’YG’+RY’G+RYG’+RGY=∑(m0,m2,m5,m6,m7)最小項概念最小項的性質(zhì)3.1CombinationallogicfunctionsandexpressionsUsingKarnaughmaptodefineacombinationallogicfunction

L=R’Y’G’+R’YG’+RY’G+RYG’+RGY=∑(m0,m2,m5,m6,m7)L=R’G’+RG+RY3.1CombinationallogicfunctionsandexpressionsalogiccircuitfordetectingTrafficlights‘Workingstatus'L=R’G’+RG+RY3.4MSIcombinationalcircuitsmodelsmall-scaleintegration，SSI<10gatesmedium-scaleintegration，MSI10-100gates（multiplexers,decoders,encoders,etc）large-scaleintegration，LSI100-10000gates（programmablelogicdevices,PLD）verylarge-scaleintegration，VLSIMillionsofgates（highperformancemicroprocessors）Multiplexer（多路轉(zhuǎn)換器）MUXd0d1d2d3d3d5d6d7ECBAyy3.4CombinationalMSIModulesDecoder/demultiplexer（譯碼器/多路分離器）3.4CombinationalMSIModulesDecoder/demultiplexer（譯碼器/多路分離器）Y0Y1Y2Y3Y4Y5Y6Y7G1G2AG2BCBA74LS138input output CBAY7Y6Y5Y4Y3Y2Y1Y000001111001100110101010111111110111111011111101111110111111011111101111110111111011111113.4CombinationalMSIModulesDecoder/demultiplexer（譯碼器/多路分離器）3.4CombinationalMSIModulesencoder（編碼器）

input output I7I6I5I4I3I2I1I0

y2

y1y0v0000011110001100110010101010000000010000000100000001000000010000000100000001000000010000000100000000111111113.4CombinationalMSI