同步时序线路分析和设计-1

AnalysisandSynthesisofSynchronousSequentialCircuitsClassificationofSequentialCircuitsSynchronousSequentialCircuits(同步时序电路):Allflip-flopsinsystemarecontrolledbyaglobalclocksignal.Thatiswhatwediscussedinthischapter.AsynchronousSequentialCircuits(异步时序电路):Allflip-flopsarenotdrivenbyoneclocksignalorthereisnoclockpulseinput.Thatis,thetransitionfromonestatetoanotherisinitiatedbythechangeintheprimaryinputs;thereisnoexternalsynchronisation(无外部同步机制).TwoBasicModelsMealy(米里型):Theoutputisafunctionofpresentstate&presentinputs;Moore(摩尔型):Theoutputcanchangeonlywhenthestatechangesandhavenothingtodowiththeinputs.Outputonlydependsonpresentstates.TwoTypicalApplicationsAnalysis(分析):Withgivencircuit,tellwhatdoesitdo?Design/Synthesis(设计/综合):Givenspecificationofcircuit,developdesigns.SomeImportantConceptsDrivenEquation(ControlEquation,ExcitingEquation)(驱动方程)TheinputofFFs,suchas:J=….;K=….;CharacteristicEquation(特征方程)BelongstooneFF,suchasQn+1=D;StateEquation(状态方程)Equationdescribingtherelationshipofpresentstate(现态)&nextstate(次态)SomeImportantConceptsStatetransitiontable(状态转移表)Statetransitiondiagram(状态转移图)XPresentStateNextStateYQ1(n)Q0(n)Q1(n+1)Q0(n+1)0000110110110111110011001100100010011111010/1000110110/10/10/11/01/11/11/0AnalysisofSynchronousSequentialCircuitsGivenCircuitsDerivetheOutputEquation&DrivenEquationsGivetheState

Transition

Table/

diagramBuildtheStateTransitionEquationTiming

diagramExplainTheLogicFuncitonExample1(analysis)Step1,GivetheOutputEquation&DrivenEquationsExample1(analysis)Step2,DerivetheStateTransitionEquationExample1(analysis)Step3,Buildthestatetable/diagram

Example1(analysis)Step3,Buildthestatetable/diagram

010/10010110/10/10/01/11/01/11/1Example1(analysis)Step4,Tellthelogicfunction由状态图可知，本例给定的时序线路也是一个可逆二进制计数器。所示电路是一个摩尔型的同步时序线路，因为该线路的状态也是由同一个CP脉冲改变的，但路线的输出仅取决于现态，而与输入无直接关系。010/10010110/10/10/01/11/01/11/1课堂练习Letusexplorethebehaviorofthecircuitinthisfigurebydevelopingatimingdiagram,statetable,andstatediagram.Thetimingdiagramshouldshowthecircuitresponsetotheinputsequencex=01101000,withthecircuitbeginninginstatey=0.Exercise(analysis)Exercise(analysis)

yx0101/00/011/00/1Yn+1/zStatetableStatediagram0=A1=BExercise(analysis)X=01101000Y=01001011Yn+1=10010111Z=01001000Exercise(analysis)01X=01101000Y=01001011Z=01001000Exercise(analysis)Y的状态变化必然发生在下降沿z则不必Step1:DerivethestatediagramStep2:Simplify(化简)thestateStep3:Encode(编码)thestateStep4:DerivetheExcitingK-map(激励卡诺图)Step5:CheckSelf-startupStep6:DrawthecircuitSteps：DesignofSequentialCircuitAcquiretheOriginalStateDiagram(原始状态图)Example1(originalstatediagram)Designan“101”serialdetector(序列检测器),givetheoriginalstatediagram(when“101”appears,theoutputZis1,otherwiseZ=0)S0:No“1”;S1:Get“1”;S2:Get“10”;S3:Get“101”;Input: 11010010101101Output: 00010000101001Example1Example2(originalstatediagram)Designan“01”serialdetector(序列检测器),givetheoriginalstatediagram(when“01”appears,theoutputZis1,otherwiseZ=0)S0:No“0”;S1:Get“0”;S2:Get“01”;Input: 11010010101101Output: 00010010101001S0S10/00/01/11/0S20/01/0Example2(originalstatediagram)Designan“01”serialdetector(序列检测器),givetheoriginalstatediagram(when“01”appears,theoutputZis1,otherwiseZ=0)S0:No“0”;S1:Get“0”;Input: 11010010101101Output: 000100101010010/0S0S10/01/11/0SimplifytheStateTableSimplifytheStateTableGenerallyspeaking,theOriginalStateTablemaynotbethemostreducedone.(someequivalentstatesmayexist)ByReducingthestatetable,wecanassignlessFlip-Flops.PrincipleofSimplificationWecanconsiders1=s2ifinanycase,theoutputofS1&S2bethesameandthenextstatebethesame(次态相等).Considers1=s2ifinanycase,theoutputofS1&S2bethesameandthenextstatebeinterleaving(次态交错)Considers1=s2ifinanycase,theoutputofS1&S2bethesameandthenextstateloop(次态循环)ThisisSameStateY\X01AB,0A,0BB,0C,1CB,0A,0ThisisStateLoopY\X01AA,1B,1BB,0C,1CC,1B,1ThisisStateInterleavingY\X01AB,1C,0BB,0C,1CB,1A,0NotEquivalentifoutputnottheSameY\X01AA,1B,1BB,0C,1CA,0B,1JustLookintothetableY\X01AE,0D,0BA,1F,0CC,0A,1DB,0A,0ED,1C,0FC,0D,1JustLookintothetableY\X01AE,0D,0BA,1F,0CC,0A,1DB,0A,0ED,1C,0FC,0D,1隐含表法化简原始状态表隐含表：直角三角形网格。网格数为总状态数减1；横向从左到右依次标注1~n-1个状态名，纵向从上到下依次标注2~n个状态名。隐含表法化简原始状态表比较结果有状态对等效、不等效、不能确定三种。等效时在相应方格填“∨”；不等效时在相应方格填“╳”，不能确定时，将次态对填入相应方格关联比较，确定等效状态对确定最大等效类，作最小化状态表EncodeStates(状态编码)EncodeStatesAssigneverystateintheReducedStateTablewithabinarycodeAssumethatthenumberofstateisN,andthenumberofFlip-FlopisK,theremustbe2K≥N.N=9,K=4N=7,K=3Withdifferentencodingmethod,theremustbedifferentcircuitrealization.PrincipleofEncoding从理论上讲，有可能找到一种确定最佳状态编码的算法，然而至今尚未获得满意而又实用的结果。对于状态表中同一输入下的相同次态所对应的现态，应给予相邻编码。所谓相邻编码，就是指各二进制代码中只有一位码不同。为方便起见，我们把这条规则简称为“次态相同，现态相邻”对于状态表中同一现态在不同输入下的次态，应给予相邻编码。该规则可简称为“同一现态，次态相邻”对状态表中输出完全相同的现态应给予相邻编码。该规则可简称为“输出相同，现态相邻”状态表中出现次数最多的状态应该分配为逻辑0EncodeStates例略。见后面设计的详细例子ExcitingK-Map(激励卡诺图)ExcitingK-MapStateassignmentStateTransitiontableUsingfalling-edgetriggeredDFFCombinationalcircuitxzQ/Q/QQDDCCCP??????Targ