Sequential Networks Implementation Techniques

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Learn about sequential networks implementation techniques including Mealy and Moore machines, excitation table procedures, state tables, logic diagrams, and more in digital systems design.

  • Sequential Networks
  • Implementation Techniques
  • Mealy Machines
  • Moore Machines
  • Digital Systems
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  1. CSE 140: Components and Design Techniques for Digital Systems Lecture 9: Sequential Networks: Implementation CK Cheng Dept. of Computer Science and Engineering University of California, San Diego 1

  2. Implementation Format and Tool Mealy & Moore Machines, Excitation Table Procedure State Table to Logic Diagram Excitation Tables FFs Examples 2

  3. Canonical Form: Mealy and Moore Machines Mealy Machine: yi(t) = fi(X(t), S(t)) Moore Machine: yi(t) = fi(S(t)) si(t+1) = gi(X(t), S(t)) x(t) x(t) y(t) y(t) C1 C2 C1 C2 CLK CLK S(t) S(t) Moore Machine Mealy Machine 3

  4. iClicker In the logic diagram below, a D flip-flop has input x and output y. A: x= Q(t), y=Q(t) B: x=Q(t+1), y=Q(t) C: x=Q(t), y=Q(t+1) D: None of the above y x Q D CLK 4

  5. Understanding Current State and Next State in a sequential circuit Yesterday is gone. Tomorrow has not yet come. We have only today. Let us begin. today Mother Teresa sunrise 5

  6. Implementation Format Canonical Form: Mealy & Moore machines State Table Netlist Tool: Excitation Table x(t) y(t) C1 C2 CLK Q(t) Q(t+1) = g(x(t), Q(t)) Circuit C1 y(t) = f(x(t), Q(t)) Circuit C2 6

  7. Implementation Tool: Excitation Table Example: State Table id x(t) Q(t) Q(t+1) 0 0 0 1 1 1 1 0 2 0 0 1 3 1 1 0 x(t) C1 Q(t) CLK Find D, T, (S R), (J K) to drive F-Fs 7

  8. Implementation Tool: Excitation Table Example: State Table id x(t) Q(t) Q(t+1) 0 0 0 1 1 1 1 0 2 0 1 1 3 1 1 0 Excitation Table x(t) Q(t) id x(t) Q(t) T(t) Q(t+1) T(t) C1 0 0 0 1 1 Q(t) 1 1 1 1 0 CLK 2 0 1 0 1 3 1 1 1 0 Example with T flip flop 8

  9. Implementation Tool: Excitation Table Implement combinational logic C1 D(t), T(t), (S(t) R(t)), (J(t) K(t)) are functions of (x,Q(t)) Example: Excitation Table x(t) Q(t) id x(t) Q(t) T(t) Q(t+1) C1 Q(t) 0 0 0 1 1 CLK 1 1 1 1 0 2 0 1 0 1 3 1 1 1 0 9

  10. Implementation: Procedure State Table => Excitation Table Problem: To implement C1, we need D(t), T(t), (S(t) R(t)), (J(t) K(t)) as functions of (x,Q(t)). 1. From state table, we have NS: Q(t+1) = g(x(t),Q(t)) 2. Excitation Table of F-Fs: The setting of D(t), T(t), (S(t) R(t)), (J(t) K(t)) to drive Q(t) to Q(t+1). 3. Combining 1 and 2, we have excitation table of C1: D(t), T(t), (S(t) R(t)), (J(t) K(t)) = h(x,Q(t)). 10

  11. Implementation: Procedure F-F State Table <=> F-F Excitation Table DTSRJK PS Q(t) T F-F NS Q(t+1) D F-F D(t)= eD(Q(t+1), Q(t)) T(t)= eT(Q(t+1), Q(t)) SR F-F S(t)= eS(Q(t+1), Q(t)) R(t)= eR(Q(t+1), Q(t)) JK F-F J(t)= eJ(Q(t+1), Q(t)) K(t)= eK(Q(t+1), Q(t)) NS Q(t+1) PS DTSRJK Q(t) 11

  12. Excitation Table State table of JK F-F: JK 00 0 1 11 1 0 10 1 1 01 0 0 0 1 Q(t+1) Q(t) Excitation table of JK F-F: Q(t+1) NS PS 0 1 0 1 0- -1 1- -0 Q(t) JK Ex: If Q(t) is 1, and Q(t+1) is 0, then JK needs to be -1. 12

  13. Excitation Tables and State Tables Excitation Tables: PSNS State Tables: 00 0 1 1 Q(t) Q(t+1) JK 10 1 1 01 0 0 11 1 0 JK 1 0 0- -1 0 1- -0 0 1 Q(t+1) Q(t) SR PSSR SR Q(t+1) PSNS 10 1 1 01 0 0 11 - - 00 0 1 1 0 0 1 0 1 10 -0 0- XY Q(t) Q(t) iClicker A.XY= -1 B. XY= 01 C. XY= 10 D.XY= 1- E. None of the above Q(t+1) 13

  14. Excitation Tables and State Tables Excitation Tables: State Tables: T T Q(t+1) PSNS PST 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 Q(t) Q(t) Q(t+1) D D Q(t+1) PSNS PSD 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 Q(t) Q(t) Q(t+1) 14

  15. Implementation: Procedure State table: y(t)= f(Q(t), x(t)), Q(t+1)= g(x(t),Q(t)) Excitation table of F-Fs: D(t)= eD(Q(t+1), Q(t)); T(t)= eT(Q(t+1), Q(t)); (S, R), or (J, K) From 1 & 2, we derive excitation table of the system D(t)= hD(x(t),Q(t))= eD(g(x(t),Q(t)),Q(t)); T(t)= hT(x(t),Q(t))= eT(g(x(t),Q(t)),Q(t)); (S, R) or (J, K). Use K-map to derive combinational logic implementation. D(t)= hD(x(t),Q(t)) T(t)= hT(x(t),Q(t)) y(t)= f(x(t),Q(t)) 1. 2. 3. 4. 15

  16. Implementation: Example Implement a JK F-F with a T F-F J Q Q Q K C1 T Q(t+1) = h(J(t),K(t),Q(t)) = J(t)Q (t)+K (t)Q(t) Implement a JK F-F: JK PSJK 00 0 1 01 0 0 10 1 1 11 1 0 0 1 Q(t) 16

  17. Example: Implement a JK flip-flop using a T flip-flop i.e. Q(t+1)(t) = JQ (t)+K Q(t) Excitation Table of T Flip-Flop Q(t+1) PSNS State table: y(t)= f(Q(t), x(t)), Q(t+1)= g(x(t),Q(t)) Excitation table of F-Fs: D(t)= eD(Q(t+1), Q(t)); T(t)= eT(Q(t+1), Q(t)); (S, R), or (J, K) 3. From 1 & 2, we derive excitation table of the system D(t)= hD(x(t),Q(t))= eD(g(x(t),Q(t)),Q(t)); T(t)= hT(x(t),Q(t))= eT(g(x(t),Q(t)),Q(t)); (S, R) or (J, K). 4. Use K-map to derive combinational logic implementation. D(t)= hD(x(t),Q(t)) T(t)= hT(x(t),Q(t)) y(t)= f(x(t),Q(t)) 1. 0 0 1 1 1 0 0 1 2. Q(t) Excitation Table of the Design J(t) 0 0 0 0 1 1 1 1 K(t) 0 0 1 1 0 0 1 1 Q(t) 0 1 0 1 0 1 0 1 Q(t+1) 0 1 0 0 1 1 1 0 T(t) 0 0 0 1 1 0 1 1 id 0 1 2 3 4 5 6 7 T(t) = Q(t) XOR ( J(t)Q (t) + K (t)Q(t)) 17

  18. Example: Implement a JK flip-flop using a T flip-flop T(J,K,Q): K 0 2 6 4 0 0 1 1 T = K(t)Q(t) + J(t)Q (t) 1 3 7 5 0 1 1 0 Q(t) J J Q T Q K 18

  19. iClicker Before state assignment, the relation of its state table and excitation table is A.One to one B.One to many C.Many to one D.Many to many E.None of the above 19

  20. Lets implement our free running 2-bit counter using T-flip flops S0 S1 S3 S2 State Table Next state S1 S2 S3 S0 PS S0 S1 S2 S3 20

  21. Lets implement our free running 2-bit counter using T-flip flops S0 S1 S3 S2 State Table with Assigned Encoding State Table Next Current 01 10 11 00 0 0 0 1 1 0 1 1 S1 S2 S3 S0 S0 S1 S2 S3 21

  22. Lets implement our free running 2-bit counter using T-flip flops Excitation table id Q1(t) 0 Q0(t) 0 T1(t) T0(t) Q1(t+1) 0 Q0(t+1) 1 0 1 0 1 1 0 2 1 0 1 1 3 1 1 0 0 22

  23. Lets implement our free running 2-bit counter using T-flip flops Excitation table id Q1(t) 0 Q0(t) 0 T1(t) 0 T0(t) 1 Q1(t+1) 0 Q0(t+1) 1 0 1 0 1 1 1 1 0 2 1 0 0 1 1 1 3 1 1 1 1 0 0 23

  24. Lets implement our free running 2-bit counter using T-flip flops Excitation table id Q1(t) 0 Q0(t) 0 T1(t) 0 T0(t) 1 Q1(t+1) 0 Q0(t+1) 1 0 1 0 1 1 1 1 0 2 1 0 0 1 1 1 3 1 1 1 1 0 0 T0(t) = T1(t) = Q0(t+1) = T0(t) Q 0(t)+T 0(t)Q0(t) Q1(t+1) = T1(t) Q 1(t)+T 1(t)Q1(t) 24

  25. Lets implement our free running 2-bit counter using T-flip flops Excitation table id Q1(t) 0 Q0(t) 0 T1(t) 0 T0(t) 1 Q1(t+1) 0 Q0(t+1) 1 0 1 0 1 1 1 1 0 2 1 0 0 1 1 1 3 1 1 1 1 0 0 T0(t) = 1 T1(t) = Q0(t) 25

  26. Free running counter with T flip flops Q0 1 Q T Q Q Q1 T Q T1 T0(t) = 1 T1(t) = Q0(t) 26

  27. Summary: Implementation Set up canonical form Mealy or Moore machine Identify the next states state diagram state table state assignment Derive excitation table Inputs of flip flops Design the combinational logic don t care set utilization 27

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