基本逻辑函数-Basic Logic Functions-

基本逻辑函数BasicLogicFunctions逻辑函数中三种最基本的逻辑运算ThreeMostFundamentalLogicOperationsinLogicFunctions主要要求：LearningObjectives:1.理解逻辑函数和逻辑变量.Understandlogicfunctionsandlogicvariables.2.掌握三种基本逻辑关系及表示方法Masterthethreebasiclogicrelationshipsandtheirrepresentations.一、逻辑函数和逻辑变量决定事物的因素（原因）为逻辑自变量，被决定的事物的结果为逻辑因变量。被概括的以某种形式表达的逻辑自变量和逻辑结果的函数关系称为逻辑函数。在逻辑代数中，逻辑变量也是用字母来表示的。逻辑变量的取值只有两个：1和0。Inlogicalalgebra,logicvariablesarealsorepresentedbyletters.Logicvariableshaveonlytwopossiblevalues:1and0.Thegeneralizedfunctionrelationshipbetweenlogicalindependentvariablesandlogicalresultsexpressedinsomeformiscalledalogicfunction.Thefactors(causes)determiningsomethingarelogicalindependentvariables,whiletheresultsofwhatisdeterminedarelogicaldependentvariables.LogicFunctionsandLogicVariables逻辑函数中三种最基本的逻辑运算ThreeMostFundamentalLogicOperationsinLogicFunctions注意:逻辑代数中的1和0不表示数量大小，仅表示两种相反的状态。

例如：开关闭合为1晶体管截至为1电位高为1

断开为0导通为0低为0Note:Inlogicalalgebra,1and0donotrepresentquantityormagnitude;theyonlyrepresenttwoopposingstates.

Forexample:Onisrepresentedas1,offas0;Atransistorinthecutoffstateis1,intheconductingstateis0;Highvoltageis1,lowvoltageis0.逻辑函数中三种最基本的逻辑运算ThreeMostFundamentalLogicOperationsinLogicFunctions“与”逻辑关系和门1.与逻辑关系"AND"logicrelationship与逻辑：决定事件发生的各条件中，所有条件都具备，事件才会发生（成立）。UABY规定:Rules:开关合为逻辑“1”Switchclosedisrepresentedaslogic"1";开关断为逻辑“0”Switchopenisrepresentedaslogic"0";灯亮为逻辑“1”Lightonisrepresentedaslogic"1";灯灭为逻辑“0”Lightoffisrepresentedaslogic"0".真值表ABY000010100111此电路实现“与”逻辑关系"AND"LogicRelationshipandGatesThe"AND"logicrelationship:Foraneventtooccur(betrue),allconditionsthatdeterminetheeventmustbesatisfied.逻辑函数中三种最基本的逻辑运算ThreeMostFundamentalLogicOperationsinLogicFunctions二、“与”逻辑关系和门

Representationofthe"AND"logicrelationship2.与逻辑关系表示式与逻辑运算规则—逻辑乘Rulesfor"AND"LogicOperations-LogicalMultiplicationY=A•B=AB

000010100111ABY真值表truthtable0•0=00•1=01•0=01•1=1真值表特点:有0则0,全1则1Truthtablefeatures:Ifthereisa"0",theresultis"0";ifallinputsare"1",theresultis"1".Rulesfor"AND"LogicOperations-LogicalMultiplication与门符号:&ABYSymbolfor"AND"gate逻辑函数中三种最基本的逻辑运算ThreeMostFundamentalLogicOperationsinLogicFunctions逻辑表达式、运算和波形图LogicalExpression,Operation,andWaveformF=A•B

1•1=11•0=00•1=00•0=0与运算可以用逻辑表达式表示为波形图Waveform读作A与B（A乘B）The"AND"operationcanbeexpressedbyalogicalexpressionasreadas"AANDB"(AmultipliedbyB)0011ABF0110三、“或”逻辑关系和或门1.“或”逻辑关系或逻辑：决定事件发生的各条件中，有一个或一个以上的条件具备，事件就会发生（成立）。UABY000011101111ABY开关合为逻辑“1”，开关断为逻辑“0”；灯亮为逻辑“1”，灯灭为逻辑“0”。设：特点:任1则1,全0则0Features:Any1conditionresultsinlogic"1";all0conditionsresultinlogic"0".Assumptions:Aswitchintheclosedpositionrepresentslogic"1",whileanopenswitchrepresentslogic"0".Alitbulbcorrespondstologic"1",andanextinguishedbulbcorrespondstologic"0."In"OR"logic,aneventoccurs(isvalid)ifoneormoreoftheconditionsthatdeterminetheeventaremet."OR"logicrelationship"OR"LogicRelationshipandORGate逻辑函数中三种最基本的逻辑运算ThreeMostFundamentalLogicOperationsinLogicFunctions真值表truthtable2.或逻辑关系表示式或逻辑运算规则—逻辑加

Y=A＋B

000011101111ABY或逻辑真值表0+0=00+1=11+0=11+1=1Rulesfor"OR"logicoperations—logicaladdition或门符号:ABY≥1SymbolforORgate:Truthtablefor"OR"logic三、“或”逻辑关系和或门"OR"LogicRelationshipandORGate逻辑函数中三种最基本的逻辑运算ThreeMostFundamentalLogicOperationsinLogicFunctions功能表、真值表和波形图FunctionTable,TruthTable,andWaveform真值表功能表FunctiontableTruthtable功能表、真值表和波形图FunctionTable,TruthTable,andWaveform波形图WaveformFtttAB四、“非”逻辑关系与非门1.“非”逻辑关系“非”逻辑"NOT"logic：决定事件发生的条件只有一个,条件不具备时事件发生（成立）。Theeventoccurs(holds)onlywhenthereisoneconditionfortheeventtohappen，条件具备时事件不发生。andtheeventdoesnotoccurwhentheconditionismet.特点:1则0,0则1真值表Truthtable0110AYYRAUFeatures:1resultsin0,0resultsin1."NOT"logicrelationship逻辑函数中三种最基本的逻辑运算ThreeMostFundamentalLogicOperationsinLogicFunctions2.非逻辑关系表示式：非逻辑—逻辑反非逻辑真值表NOTLogicTruthTable

AY0110

运算规则：Operationrules:

0＝11＝0非逻辑关系表示式:Y＝ANOTLogic-LogicalNOTNOTLogicRelationshipExpression:逻辑函数中三种最基本的逻辑运算ThreeMostFundamentalLogicOperationsinLogicFunctions三、“或”逻辑关系和或门"OR"LogicRelationshipandORGateFttA波形图逻辑符号非运算可以用逻辑表达式表示为F=A

0=11=0(读作A非)(ReadasA-bar)LogicSymbolWaveformTheNOToperationcanbeexpressedusingalogicexpressionas非运算的表示RepresentationofNOTOperation主要要求：1.含有两种或两种以上逻辑运算的逻辑函数称为复合逻辑函数。Logicfunctionsthatinvolvetwoormoretypesoflogicoperationsareknownascompoundlogicfunctions.2.掌握几种常见的复合函数例如：与非、或非、与或非、异或、同或等。FamiliaritywithseveralcommoncompoundfunctionssuchasNAND,NOR,AND-OR-INVERT,XOR,XNOR,etc.复合逻辑函数CompoundLogicFunctions与非逻辑(NAND)先与后非若有

0

出

1、若全

1

出

0由基本逻辑运算组合而成100011YA

B110011Thesecompoundfunctionsareformedbycombiningbasiclogicoperations.NANDLogic(AND-NOT):FirstAND,thenNOTIfthere'sa0,itresultsin1,ifallinputsare1,itresultsin0.复合逻辑函数CompoundLogicFunctions或非逻辑(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复合逻辑函数CompoundLogicFunctions由基本逻辑运算组合而成Thesecompoundfunctionsareformedbycombiningbasiclogicoperations.与或非逻辑(AND–OR–INVERT)先与后或再非可以有二个以上的输入变量Thesefunctionscaninvolvemorethantwoinputvariables.XNORLogic(Exclusive-NOR,i.e.,ExclusiveORNOT)ANDthenNOR复合逻辑函数C