1. CSE 140 Lecture 10 Sequential Networks: Implementation
Professor CK Cheng
CSE Dept.
UC San Diego

2. Implementation
Format and Tool
Procedure
Excitation Tables
Example

3. Canonical Form: Mealy and Moore Machines
x(t)
Combinational
Logic
y(t)
CLK
x(t) C2
y(t)
x(t) C1 C2
y(t) C1
CLK
CLK

4. 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

5. iClicker
The advantage of Moore machine over Mealy machine is that for Moore machine,
the circuit is smaller
the circuit is faster
the input is synchronized with clock
the output is synchronized with clock
None of the above

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

7. Implementation: Procedure
State Table => Excitation Table
Given a state table, we have
NS: Q(t+1) = h(X(t),Q(t))
We want to derive
D(t), T(t), (S(t) R(t)), (J(t) K(t)) as functions of (X,Q(t)).
We implement D, T, (S R), (J K) as combinational logic.

8. Implementation: Procedure
F-F State Table <=> F-F Excitation Table W PS NS NS PS W W:
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))

9. Implementation: Procedure
State table: y(t)= f(Q(t), x(t)), Q(t+1)= h(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)= gD(Q(t), x(t))= eD(h(x(t),Q(t)),Q(t));
T(t)= gT(Q(t), x(t))= eT(h(x(t),Q(t)),Q(t));
(S, R) or (J, K).
Use K-map to derive optional combinational logic implementation.
T(t)= gT(Q(t), x(t))
y(t)= f(Q(t), x(t))

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

11. Excitation Tables and State TablesSR SR
Q(t+1) NS SR PS 0- 01 1 10 -0 PS 00 1 01 10 1 11 - 1 1
Q(t)
Q(t)
Q(t+1) T T
Q(t+1) NS T PS 1 1 PS 1 1 1 1
Q(t)
Q(t)
Q(t+1)

12. Excitation Tables and State TablesJK JK
Q(t+1) NS JK PS 0- -1 1 1- -0 PS 00 1 01 10 1 11 1 1 1
Q(t)
Q(t)
Q(t+1) D D
Q(t+1) NS D PS 1 PS 1 1 1
Q(t)
Q(t)
Q(t+1)

13. iClicker
Given a flip-flop, 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

14. Implementation: Example Implement a JK F-F with a T F-FQ Q’ C1 J K T
State Table
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)

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

16. 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