基本邏輯函數(shù)-Basic Logic Functions-

基本邏輯函數(shù)BasicLogicFunctions邏輯函數(shù)中三種最基本的邏輯運(yùn)算ThreeMostFundamentalLogicOperationsinLogicFunctions主要要求：LearningObjectives:1.理解邏輯函數(shù)和邏輯變量.Understandlogicfunctionsandlogicvariables.2.掌握三種基本邏輯關(guān)系及表示方法Masterthethreebasiclogicrelationshipsandtheirrepresentations.一、邏輯函數(shù)和邏輯變量決定事物的因素（原因）為邏輯自變量，被決定的事物的結(jié)果為邏輯因變量。被概括的以某種形式表達(dá)的邏輯自變量和邏輯結(jié)果的函數(shù)關(guān)系稱為邏輯函數(shù)。在邏輯代數(shù)中，邏輯變量也是用字母來(lái)表示的。邏輯變量的取值只有兩個(gè)：1和0。Inlogicalalgebra,logicvariablesarealsorepresentedbyletters.Logicvariableshaveonlytwopossiblevalues:1and0.Thegeneralizedfunctionrelationshipbetweenlogicalindependentvariablesandlogicalresultsexpressedinsomeformiscalledalogicfunction.Thefactors(causes)determiningsomethingarelogicalindependentvariables,whiletheresultsofwhatisdeterminedarelogicaldependentvariables.LogicFunctionsandLogicVariables邏輯函數(shù)中三種最基本的邏輯運(yùn)算ThreeMostFundamentalLogicOperationsinLogicFunctions注意:邏輯代數(shù)中的1和0不表示數(shù)量大小，僅表示兩種相反的狀態(tài)。

例如：開(kāi)關(guān)閉合為1晶體管截至為1電位高為1

斷開(kāi)為0導(dǎo)通為0低為0Note:Inlogicalalgebra,1and0donotrepresentquantityormagnitude;theyonlyrepresenttwoopposingstates.

Forexample:Onisrepresentedas1,offas0;Atransistorinthecutoffstateis1,intheconductingstateis0;Highvoltageis1,lowvoltageis0.邏輯函數(shù)中三種最基本的邏輯運(yùn)算ThreeMostFundamentalLogicOperationsinLogicFunctions“與”邏輯關(guān)系和門(mén)1.與邏輯關(guān)系"AND"logicrelationship與邏輯：決定事件發(fā)生的各條件中，所有條件都具備，事件才會(huì)發(fā)生（成立）。UABY規(guī)定:Rules:開(kāi)關(guān)合為邏輯“1”Switchclosedisrepresentedaslogic"1";開(kāi)關(guān)斷為邏輯“0”Switchopenisrepresentedaslogic"0";燈亮為邏輯“1”Lightonisrepresentedaslogic"1";燈滅為邏輯“0”Lightoffisrepresentedaslogic"0".真值表ABY000010100111此電路實(shí)現(xiàn)“與”邏輯關(guān)系"AND"LogicRelationshipandGatesThe"AND"logicrelationship:Foraneventtooccur(betrue),allconditionsthatdeterminetheeventmustbesatisfied.邏輯函數(shù)中三種最基本的邏輯運(yùn)算ThreeMostFundamentalLogicOperationsinLogicFunctions二、“與”邏輯關(guān)系和門(mén)

Representationofthe"AND"logicrelationship2.與邏輯關(guān)系表示式與邏輯運(yùn)算規(guī)則—邏輯乘Rulesfor"AND"LogicOperations-LogicalMultiplicationY=A?B=AB

000010100111ABY真值表truthtable0?0=00?1=01?0=01?1=1真值表特點(diǎn):有0則0,全1則1Truthtablefeatures:Ifthereisa"0",theresultis"0";ifallinputsare"1",theresultis"1".Rulesfor"AND"LogicOperations-LogicalMultiplication與門(mén)符號(hào):&ABYSymbolfor"AND"gate邏輯函數(shù)中三種最基本的邏輯運(yùn)算ThreeMostFundamentalLogicOperationsinLogicFunctions邏輯表達(dá)式、運(yùn)算和波形圖LogicalExpression,Operation,andWaveformF=A?B

1?1=11?0=00?1=00?0=0與運(yùn)算可以用邏輯表達(dá)式表示為波形圖Waveform讀作A與B（A乘B）The"AND"operationcanbeexpressedbyalogicalexpressionasreadas"AANDB"(AmultipliedbyB)0011ABF0110三、“或”邏輯關(guān)系和或門(mén)1.“或”邏輯關(guān)系或邏輯：決定事件發(fā)生的各條件中，有一個(gè)或一個(gè)以上的條件具備，事件就會(huì)發(fā)生（成立）。UABY000011101111ABY開(kāi)關(guān)合為邏輯“1”，開(kāi)關(guān)斷為邏輯“0”；燈亮為邏輯“1”，燈滅為邏輯“0”。設(shè)：特點(diǎn):任1則1,全0則0Features:Any1conditionresultsinlogic"1";all0conditionsresultinlogic"0".Assumptions:Aswitchintheclosedpositionrepresentslogic"1",whileanopenswitchrepresentslogic"0".Alitbulbcorrespondstologic"1",andanextinguishedbulbcorrespondstologic"0."In"OR"logic,aneventoccurs(isvalid)ifoneormoreoftheconditionsthatdeterminetheeventaremet."OR"logicrelationship"OR"LogicRelationshipandORGate邏輯函數(shù)中三種最基本的邏輯運(yùn)算ThreeMostFundamentalLogicOperationsinLogicFunctions真值表truthtable2.或邏輯關(guān)系表示式或邏輯運(yùn)算規(guī)則—邏輯加

Y=A＋B

000011101111ABY或邏輯真值表0+0=00+1=11+0=11+1=1Rulesfor"OR"logicoperations—logicaladdition或門(mén)符號(hào):ABY≥1SymbolforORgate:Truthtablefor"OR"logic三、“或”邏輯關(guān)系和或門(mén)"OR"LogicRelationshipandORGate邏輯函數(shù)中三種最基本的邏輯運(yùn)算ThreeMostFundamentalLogicOperationsinLogicFunctions功能表、真值表和波形圖FunctionTable,TruthTable,andWaveform真值表功能表FunctiontableTruthtable功能表、真值表和波形圖FunctionTable,TruthTable,andWaveform波形圖WaveformFtttAB四、“非”邏輯關(guān)系與非門(mén)1.“非”邏輯關(guān)系“非”邏輯"NOT"logic：決定事件發(fā)生的條件只有一個(gè),條件不具備時(shí)事件發(fā)生（成立）。Theeventoccurs(holds)onlywhenthereisoneconditionfortheeventtohappen，條件具備時(shí)事件不發(fā)生。andtheeventdoesnotoccurwhentheconditionismet.特點(diǎn):1則0,0則1真值表Truthtable0110AYYRAUFeatures:1resultsin0,0resultsin1."NOT"logicrelationship邏輯函數(shù)中三種最基本的邏輯運(yùn)算ThreeMostFundamentalLogicOperationsinLogicFunctions2.非邏輯關(guān)系表示式：非邏輯—邏輯反非邏輯真值表NOTLogicTruthTable

AY0110

運(yùn)算規(guī)則：Operationrules:

0＝11＝0非邏輯關(guān)系表示式:Y＝ANOTLogic-LogicalNOTNOTLogicRelationshipExpression:邏輯函數(shù)中三種最基本的邏輯運(yùn)算ThreeMostFundamentalLogicOperationsinLogicFunctions三、“或”邏輯關(guān)系和或門(mén)"OR"LogicRelationshipandORGateFttA波形圖邏輯符號(hào)非運(yùn)算可以用邏輯表達(dá)式表示為F=A

0=11=0(讀作A非)(ReadasA-bar)LogicSymbolWaveformTheNOToperationcanbeexpressedusingalogicexpressionas非運(yùn)算的表示RepresentationofNOTOperation主要要求：1.含有兩種或兩種以上邏輯運(yùn)算的邏輯函數(shù)稱為復(fù)合邏輯函數(shù)。Logicfunctionsthatinvolvetwoormoretypesoflogicoperationsareknownascompoundlogicfunctions.2.掌握幾種常見(jiàn)的復(fù)合函數(shù)例如：與非、或非、與或非、異或、同或等。FamiliaritywithseveralcommoncompoundfunctionssuchasNAND,NOR,AND-OR-INVERT,XOR,XNOR,etc.復(fù)合邏輯函數(shù)CompoundLogicFunctions與非邏輯(NAND)先與后非若有

0

出

1、若全

1

出

0由基本邏輯運(yùn)算組合而成100011YA

B110011Thesecompoundfunctionsareformedbycombiningbasiclogicoperations.NANDLogic(AND-NOT):FirstAND,thenNOTIfthere'sa0,itresultsin1,ifallinputsare1,itresultsin0.復(fù)合邏輯函數(shù)CompoundLogicFunctions或非邏輯(NOR)先或后非若有

1

出

0、若全

0

出

1011100001YA

B010XORLogic(Exclusive–OR)Ifthere'sa1,itresultsin0;ifallinputsare0,itresultsin1.FirstOR,thenNOT復(fù)合邏輯函數(shù)CompoundLogicFunctions由基本邏輯運(yùn)算組合而成Thesecompoundfunctionsareformedbycombiningbasiclogicoperations.與或非邏輯(AND–OR–INVERT)先與后或再非可以有二個(gè)以上的輸入變量Thesefunctionscaninvolvemorethantwoinputvariables.XNORLogic(Exclusive-NOR,i.e.,ExclusiveORNOT)ANDthenNOR復(fù)合邏輯函數(shù)C