1Synchronous Sequential NetworkAnalysisSynthesis2Synchronous Sequential Network - ANALYSISTransition TableExcitation Table3EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04Mealy and Moore Machinez Q+ = f(X,Q)z Mealy: Z = g(X,Q)z Moore: Z = g(Q)NSQ+PSInputZOutputSCClockQX4EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04AnalysisFig 1.XX’ZX’XD1D2CDDCQQQQQ1Q1’Q2Q2’CLOCKFF1FF25EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04AnalysisExcitation and Output ExpressionFig 1 => D1 = x’Q2’ + Q1’Q2D2= xQ1’ + Q1’Q2z=x’Q1 + x Q1’Q2’6EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04Characteristic Equation: D f/f => Q+= DSubstitute the excitation equation into the characteristic equation to obtain the transition equationsQ1+= D1=> Q1+= x’Q2+ Q1’Q2Q2+= D2=> Q2+= xQ1’ + Q1’Q2Transition Equation7EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04From Transition Equations, obtain the transition tablex = 0 x = 10 10 01 01 0x = 0 x = 11 0 0 11 1 1 11 0 0 00 0 0 00 00 11 01 1Output ZNS (Q1+,Q2+)PS(Q1,Q2)Transition Table8EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04An alternative way to generate the transition table (with transition equations) is to construct the excitation table0 10 10 01 01 00 11 0 0 11 1 1 11 0 0 00 0 0 00 00 11 01 1Output ZExcitation(D1,D2)PS(Q1,Q2)Excitation Tables9EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04Using Truth Table for f/f we derive the transition table from the excitation tableDQQ+000010101111Excitation Tables10EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04State TablesState assignment : 00 – A01 – B10 – C11 – D0 10 01 01 0C BD DC A A AABCDOutputx = 0 x = 1NSx = 0 x = 1PSC/0 B/1D/0 D/0C/1 A/0 A/1 A/0ABCDNS/zx = 0 x = 1PS11EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04State Diagram1/10/0,1/00/11/01/00/0ABCD0/1Fig 1.12EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04Fig 2.AnalysisCCCLOCKFF2Q2’Q1’Q1QQQQZ1Z2K2JKJ2K1yy’xyxxJ1JKyyx’FF113EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04Excitation and Output Expression=> J1= y , K1= y + xQ2’J2= xQ1’ + x’yQ1, K2= xy’ + yQ1z1= Q1Q2’, z2= Q1+ Q2’Analysis14EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04Transition EquationCharacteristic Equation: JK f/f => Q+= JQ’ + K’QSubstitute the excitation equation into the characteristic equation to obtain the transition equationsQ1+= J1Q1’ + K1’Q1= yQ1’ + (y + xQ2’)’Q1= yQ1’ + x’y’Q1+ y’Q1Q2Q2+= J2Q2’+ K2’Q2= (xQ1’ + x’yQ1)Q2’ + (xy’ + yQ1)’Q2= xQ1’Q2’ + x’yQ1Q2’ +x’y’Q2+ x’Q1’Q2+ yQ1’Q215EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04From Transition Equations, obtain the transition table 1 11 10 00 00 10 00 01 01 01 10 10 00 00 11 01 10 10 01 10 11 11 00 10 00 00 11 01 1Output Z1 Z2NS (Q1+,Q2+)PS(Q1,Q2)Transition Table16EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04An alternative way to generate the transition table (with transition equations) is to construct the excitation table11, 1011, 1011, 0111, 0101, 1100, 1101, 0100, 0111, 0011, 0011, 1111, 1100, 0000, 0000, 0000, 000 10 01 10 11 11 00 10 00 00 11 01 1Output Z1 Z2Excitation J1K1 J2 K2PSQ1,Q2Excitation Tables17EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04Using Truth Table for f/f we derive the transition table from the excitation tableJ KQQ+00000011010001101001101111011110Excitation Tables18EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 040 10 01 10 1DDAABAACCDBAABCDABCD1 01 10 10 0Zz1 z2NSPSState Table19EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04State DiagramC/11A/01B/00D/0111110001,10000011010110,1101,101000Fig 2.20EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04The Analysis ProcessCircuit DiagramAssign State & Excitation VariablesExcitation & Output EquationTransition EquationExcitation TableTransition TableState TableState Diagram21Synchronous Sequential Network - SYNTHESIS22EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04Synthesis of Sync. Seq. CircuitA BD C0/01/01/10/00/01/01/00/123EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04a. State Tableb. Transition Table10/011/11010/001/01111/100/00101/000/0000010D11C01B00Ay1y2StateState TableTransition Tabley1y2x24EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04c. Output K-map011000111001000000Output K-mapy1y2x25EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04d. Select Device111010111001000000Excitation K-mapy1y2x011001111001100000Excitation K-mapy1y2xD1= y1D2= y226EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04e. Logic Equations212111122211yyxyyxzyxyxyxDxyyyD+=⊕=+=+=27EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04f. Logic DiagramD2CLKQ/QD1CLKQ/Qxy2not y2y1zCLKnot y128EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04z Memory Device Type => Excitation Mapz Example: J/K Flip FlopQQ+J K000d011d10d111d0Different Device29EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis Lecture 04c. Output K-map011000111001000000Output K-mapy1y2x30EE270 Synchronous Sequential Network - ANALYSIS Dr. Tri Caohuu © 2006 Andy Davis