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

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

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) C1 C2
y(t) C1 C2
y(t)
CLK
CLK
S(t)
S(t)
Mealy Machine
Moore Machine

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 D y
CLK x Q

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.”
― Mother Teresa
today
sunrise

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

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

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

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) C1
CLK
Q(t) id
x(t)
Q(t)
T(t)
Q(t+1) 1 2 3
Q(t)

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)).

11. Implementation: Procedure
F-F State Table <=> F-F Excitation Table
DTSRJK PS
Q(t)
NS Q(t+1)
D F-F
D(t)= eD(Q(t+1), Q(t))
T F-F
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
Q(t)
DTSRJK

12. Excitation Table State table of JK F-F: 00 1 01 10 11 Q(t) Q(t+1) JK1 01 10 11
Q(t)
Q(t+1) JK
Excitation table of JK F-F: 0- -1 1 1- -0 PS NS
Q(t)
Q(t+1) JK
Ex: If Q(t) is 1, and Q(t+1) is 0, then JK needs to be -1.

13. Excitation Tables and State Tables
Q(t+1) JK 00 1 10 11
Q(t)
Q(t+1) NS 01 JK 0- -1 1 1- -0 PS 1
Q(t) SR 0- XY 1 10 -0 PS NS
Q(t)
Q(t+1) SR 00 1 01 PS SR
Q(t)
Q(t+1) 10 11 -
iClicker
XY= -1
XY= 01
XY= 10
XY= 1-
None of the above

14. Excitation Tables and State Tables1 PS NS
Q(t)
Q(t+1) T D
Q(t+1) D NS D PS 1 PS 1 1 1
Q(t)
Q(t)
Q(t+1)

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))

16. Implementation: Example Implement a JK F-F with a T F-FQ Q’ C1 J K T Q
Implement a JK F-F:
Q(t+1) = h(J(t),K(t),Q(t)) = J(t)Q’(t)+K’(t)Q(t) JK JK PS 00 1 01 10 1 11 1 1
Q(t)

17. Example: Implement a JK flip-flop using a T flip-flop
Excitation Table of T Flip-Flop
i.e. Q(t+1)(t) = JQ’(t)+K’Q(t) 1 PS NS
Q(t)
Q(t+1)
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))
Excitation Table of the Design id 1 2 3 4 5 6 7
J(t)
K(t)
Q(t)
Q(t+1)
T(t)
T(t) = Q(t) XOR ( J(t)Q’(t) + K’(t)Q(t))

18. Example: Implement a JK flip-flop using a T flip-flop
T(J,K,Q): K
T = K(t)Q(t) + J(t)Q’(t)
Q(t) J J Q Q’ T K

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

20. Let’s implement our free running 2-bit counter using T-flip flops
State Table S0 S1 S2 S3 PS
Next state

21. Let’s implement our free running 2-bit counter using T-flip flops
State Table with Assigned
Encoding
State Table
0 0
0 1
1 0
1 1
Current 01 10 11 00 S0 S1 S2 S3
Next

22. Let’s implement our free running 2-bit counter using T-flip flops
Excitation table id
Q1(t)
Q0(t)
T1(t)
T0(t)
Q1(t+1)
Q0(t+1) 1 2 3

23. Let’s implement our free running 2-bit counter using T-flip flops
Excitation table id
Q1(t)
Q0(t)
T1(t)
T0(t)
Q1(t+1)
Q0(t+1) 1 2 3

24. Let’s implement our free running 2-bit counter using T-flip flops
Excitation table id
Q1(t)
Q0(t)
T1(t)
T0(t)
Q1(t+1)
Q0(t+1) 1 2 3
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)

25. Let’s implement our free running 2-bit counter using T-flip flops
Excitation table id
Q1(t)
Q0(t)
T1(t)
T0(t)
Q1(t+1)
Q0(t+1) 1 2 3
T0(t) = 1
T1(t) = Q0(t)

26. Free running counter with T flip flopsQ Q’ Q0 Q1 1 T1
T0(t) = 1
T1(t) = Q0(t)

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