Analysis and Design of Sequential Circuits: Examples
Transcript of Analysis and Design of Sequential Circuits: Examples
![Page 1: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/1.jpg)
COSC3410
Analysis and Design of Sequential Circuits:
Examples
J. C. Huang Department of Computer Science
University of Houston
Sequential machine slide 1
![Page 2: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/2.jpg)
combi-national circuit
inputs outputs
memory elements
The block diagram of a sequential circuit
Sequential machine slide 2
![Page 3: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/3.jpg)
comb. network
B'B
A'A
D
D
y = (A+B)x'x
DA=xA+xB
DB=xA'
Block diagram for the sequential circuit shown in Fig. 6-16
Sequential machine slide 3
![Page 4: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/4.jpg)
comb. network
B'B
A'A
JK
JK
x
Sequential circuit implemented with JK flip-flops (Fig. 6-19)
JA = B KA = Bx' JB = x'
KB = A'x + Ax'
KAJAKBJB
Sequential machine slide 4
![Page 5: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/5.jpg)
An example analysis problem: Given the sequential circuit depicted below, construct the state table that describe its behavior.
comb. network
B'B
A'A
JK
JK
xKAJAKBJB JA = B
KA = Bx' JB = x'
KB = A'x + Ax'
next state present state x = 0 x = 1
A(t)B(t) 0 0
A(t+1)B(t+1) ?
A(t+1)B(t+1) ?
0 1 ? ? 1 0 ? ? 1 1 ? ?
Sequential machine slide 5
![Page 6: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/6.jpg)
Steps involved: 1. Construct the truth table of the combinational network to
determine the output and the input to the flip-flops. 2. Use the characteristic table of the flip-flops to determine the
next states.
Sequential machine slide 6
![Page 7: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/7.jpg)
comb. network
B'B
A'A
JK
JK
x
Sequential circuit implemented with JK flip-flops (Fig. 6-19)
JA = B KA = Bx' JB = x'
KB = A'x + Ax'
KAJAKBJB
Step 1: construct the truth table of the combinational network.
x A B JA KA JB KB0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0
Sequential machine slide 7
![Page 8: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/8.jpg)
Step 2: extend the truth table to inclues contents of flip-flops at time t+1.
x A B JA KA JB KB A(t+1) B(t+1) 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0
Sequential machine slide 8
![Page 9: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/9.jpg)
Step 2.1: find A(t+1), with the help of a characteristic table.
x A B JA KA JB KB A(t+1) B(t+1) 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1
The characteristic table of a JK flip-flop
J K Q(t+1) 0 0 Q(t) no change 0 1 0 reset 1 0 1 set 1 1 Q'(t) complement
Sequential machine slide 9
![Page 10: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/10.jpg)
Step 2.2: find B(t+1), with the help of a characteristic table.
x A B JA KA JB KB A(t+1) B(t+1) 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1
The characteristic table of a JK flip-flop
J K Q(t+1) 0 0 Q(t) no change 0 1 0 reset 1 0 1 set 1 1 Q'(t) complement
Sequential machine slide 10
![Page 11: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/11.jpg)
Step 2.3: final step.
x A B JA KA JB KB A(t+1) B(t+1) 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1
Reconstruct the state table to yield
next state present state x = 0 x = 1
A(t)B(t) 0 0
A(t+1)B(t+1) 0 1
A(t+1)B(t+1) 0 0
0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1
Sequential machine slide 11
![Page 12: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/12.jpg)
Mealy and Moore Models There are two models of sequential circuit: Mealy Model: the outputs are functions of both the present states and inputs. Moore Model: the outputs are a function of the present state only. Example:
Sequential machine slide 12
![Page 13: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/13.jpg)
State Reduction
Two states are said to be equivalent if, for each possible single input, they give
exactly the same output and send the circuit either to the same state or to an
equivalent state.
When two states are equivalent in this sense, one of them can be removed without
altering the input-output relations.
Sequential machine slide 13
![Page 14: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/14.jpg)
Design Steps
1. Obtain the word description of the desired circuit behavior.
2. Construct the state table of the desired circuit.
3. Reduce the number of state to the extent possible (state reduction).
4. Assign a bit pattern to each state (state assignment).
5. Determine the no. of flip-flops needed and assign a letter symbol to each.
6. Choose the type of flip-flop to be used.
7. Derive the truth table of the required combinational circuit from the state table.
8. Simplify the combinational circuit.
9. Draw the logic diagram.
Sequential machine slide 14
![Page 15: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/15.jpg)
Design Example:
Suppose we are given a word description of the desired circuit behavior, and it is
translated into the following state table (Step 2):
present state
next state output
x=0 x=1 x=0 x=1 a f b 0 0
b d c 0 0
c f e 0 0
d g a 1 0
e d c 0 0
f g d 0 1
g g h 0 1
h g a 1 0
Sequential machine slide 15
![Page 16: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/16.jpg)
Design Example:
The number of state can be reduced to 4 (Step 3):
present state
next state output
x=0 x=1 x=0 x=1 a f b 0 0
b d a 0 0
b
d f a 1 0
a
f f d 0 1
d
Sequential machine slide 16
![Page 17: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/17.jpg)
Design Example:
The reduced state table (State 3):
present state
next state output
x=0 x=1 x=0 x=1 a f b 0 0
b d a 0 0
d f a 1 0
f f d 0 1
Sequential machine slide 17
![Page 18: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/18.jpg)
Design Example:
A possible state assignment (State 4):
present state
next state output
x=0 x=1 x=0 x=1 a f b 0 0
b d a 0 0
d f a 1 0
f f d 0 1
00 → a 01 → b 10 → d 11 → f
present state
next state output
x=0 x=1 x=0 x=1 A B
0 0
A(t+1)B(t+1)
1 1
A(t+1)B(t+1)
0 1
y(t)
0
y(t)
0
0 1 1 0 0 0 0 0
1 0 1 1 0 0 1 0
1 1 1 1 1 0 0 1
Sequential machine slide 18
![Page 19: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/19.jpg)
Design Example
This state table can be implemented by a sequential circuit of the form depicted
below using D type flip-flops (Steps 5 and 6):
comb. network
B'B
A'A
D
D
y=?x
DA=?
DB=?
Sequential machine slide 19
![Page 20: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/20.jpg)
Reconstruct the state table
present state
next state output
x=0 x=1 x=0 x=1 A B
0 0
A(t+1)B(t+1)
1 1
A(t+1)B(t+1)
0 1
y(t)
0
y(t)
0
0 1 1 0 0 0 0 0
1 0 1 1 0 0 1 0
1 1 1 1 1 0 0 1
in preparation for expanding it into a truth table of the combinational network
required (Step 7):
x A(t) B(t) A(t+1) B(t+1) y(t)
0 0 0 1 1 0
0 0 1 1 0 0
0 1 0 1 1 1
0 1 1 1 1 0
1 0 0 0 1 0
1 0 1 0 0 0
1 1 0 0 0 0
1 1 1 1 0 1
Sequential machine slide 20
![Page 21: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/21.jpg)
Expand the state table into the truth table of the combinational network (Step 7):
x A(t) B(t) A(t+1) B(t+1) DA DB y(t)
0 0 0 1 1 1 0
0 0 1 1 0 1 0
0 1 0 1 1 1 1
0 1 1 1 1 1 0
1 0 0 0 1 0 0
1 0 1 0 0 0 0
1 1 0 0 0 0 0
1 1 1 1 0 1 1
Excitation table of a D type flip-flop Q(t) Q(t+1) D(t)
0 0 0 0 1 1 1 0 0 1 1 1
Sequential machine slide 21
![Page 22: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/22.jpg)
Expand the state table into the truth table of the combinational network (Step 7):
x A(t) B(t) A(t+1) B(t+1) DA DB y(t)
0 0 0 1 1 1 1 0
0 0 1 1 0 1 0 0
0 1 0 1 1 1 1 1
0 1 1 1 1 1 1 0
1 0 0 0 1 0 1 0
1 0 1 0 0 0 0 0
1 1 0 0 0 0 0 0
1 1 1 1 0 1 0 1
Excitation table of a D type flip-flop Q(t) Q(t+1) D(t)
0 0 0 0 1 1 1 0 0 1 1 1
Sequential machine slide 22
![Page 23: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/23.jpg)
Simplify the Boolean functions that describe the outputs of the combinational network (Step 8):
A'B' A'B AB AB'
x' 1 1 1 1
x 0 0 1 0 DA = x' + AB
A'B' A'B AB AB'
x' 1 0 1 1
x 1 0 0 0 DB = x'A + A'B'
A'B' A'B AB AB'
x' 0 0 0 1
x 0 0 1 0 y = x'AB' + xAB
Sequential machine slide 23
![Page 24: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/24.jpg)
Design Example
This state table can be implemented by a sequential circuit of the form depicted
below using JK flip-flops (Steps 5 and 6):
comb. network
B'B
A'A
JK
JK
xKA=?JA=?KB=?JB=?
y=?
Sequential machine slide 24
![Page 25: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/25.jpg)
Again, start with the state table:
x A(t) B(t) A(t+1) B(t+1) y(t)
0 0 0 1 1 0
0 0 1 1 0 0
0 1 0 1 1 1
0 1 1 1 1 0
1 0 0 0 1 0
1 0 1 0 0 0
1 1 0 0 0 0
1 1 1 1 0 1
Sequential machine slide 25
![Page 26: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/26.jpg)
In preparation for constructing the truth table of the required combinational circuit,
expand the state table to include the columns for inputs to the flip-flops:
x A(t) B(t) A(t+1) B(t+1) JA KA JB KB y(t)
0 0 0 1 1 0
0 0 1 1 0 0
0 1 0 1 1 1
0 1 1 1 1 0
1 0 0 0 1 0
1 0 1 0 0 0
1 1 0 0 0 0
1 1 1 1 0 1
Sequential machine slide 26
![Page 27: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/27.jpg)
With the help of an excitation table find inputs to flip-flop A (Step 7):
x A(t) B(t) A(t+1) B(t+1) JA KA JB KB y(t)
0 0 0 1 1 1 X 0
0 0 1 1 0 1 X 0
0 1 0 1 1 X 0 1
0 1 1 1 1 X 0 0
1 0 0 0 1 0 X 0
1 0 1 0 0 0 X 0
1 1 0 0 0 X 1 0
1 1 1 1 0 X 0 1
Excitation table of a JK flip-flop Q(t) Q(t+1) J(t) K(t)
0 0 0 X 0 1 1 X 1 0 X 1 1 1 X 0
Sequential machine slide 27
![Page 28: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/28.jpg)
With the help of an excitation table find inputs to flip-flop B (Step 7):
x A(t) B(t) A(t+1) B(t+1) JA KA JB KB y(t)
0 0 0 1 1 1 X 1 X 0
0 0 1 1 0 1 X X 1 0
0 1 0 1 1 X 0 1 X 1
0 1 1 1 1 X 0 X 0 0
1 0 0 0 1 0 X 1 X 0
1 0 1 0 0 0 X X 1 0
1 1 0 0 0 X 1 0 X 0
1 1 1 1 0 X 0 X 1 1
Excitation table of a JK flip-flop Q(t) Q(t+1) J(t) K(t)
0 0 0 X 0 1 1 X 1 0 X 1 1 1 X 0
Sequential machine slide 28
![Page 29: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/29.jpg)
Simplify the outputs of the combinational network (Step 8):
A'B' A'B AB AB'
x' 1 1 X X
x 0 0 X X JA = x'
A'B' A'B AB AB'
x' X X 0 0
x X X 0 1 KA = xB'
A'B' A'B AB AB'
x' 1 X X 1
x 1 X X 0 JB = x' + A'
A'B' A'B AB AB'
x' X 1 0 X
x X 1 1 X KB = x + A'
A'B' A'B AB AB'
x' 0 0 0 1
x 0 0 1 0 y = x'AB' + xAB
Sequential machine slide 29
![Page 30: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/30.jpg)
Design of a 4-bit synchronous up counter The state table
present
state (at time t)
next state
(at t+1) A4 A3 A2 A1
0 0 0 0 A4 A3 A2 A1
0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0
Sequential machine slide 30
![Page 31: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/31.jpg)
The block diagram
JK
A1
A'1
JK
A2
A'2
JK
A3
A'3
JK
A4
A'4
combinational network
KA4
JA1
CP
Sequential machine slide 31
![Page 32: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/32.jpg)
The excitation function for the four JK flip-flops
present state
(at time t)
next state
(at t+1)
JA1
KA1
JA2
KA2
JA3
KA3
JA4
KA4
A4 A3 A2 A1 0 0 0 0
A4 A3 A2 A1 0 0 0 1
1
X
0
X
0
X
0
X
0 0 0 1 0 0 1 0 X 1 1 X 0 X 0 X 0 0 1 0 0 0 1 1 1 X X 0 0 X 0 X 0 0 1 1 0 1 0 0 X 1 X 1 1 X 0 X 0 1 0 0 0 1 0 1 1 X 0 X X 0 0 X 0 1 0 1 0 1 1 0 X 1 1 X X 0 0 X 0 1 1 0 0 1 1 1 1 X X 0 X 0 0 X 0 1 1 1 1 0 0 0 X 1 X 1 X 1 1 X 1 0 0 0 1 0 0 1 1 X 0 X 0 X X 0 1 0 0 1 1 0 1 0 X 1 1 X 0 X X 0 1 0 1 0 1 0 1 1 1 X X 0 0 X X 0 1 0 1 1 1 1 0 0 X 1 X 1 1 X X 0 1 1 0 0 1 1 0 1 1 X 0 X X 0 X 0 1 1 0 1 1 1 1 0 X 1 1 X X 0 X 0 1 1 1 0 1 1 1 1 1 X X 0 X 0 X 0 1 1 1 1 0 0 0 0 X 1 X 1 X 1 X 1
Sequential machine slide 32
![Page 33: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/33.jpg)
From the truth table we see that the desired inputs to the flip-flops can be
simplified to
JA1 = 1 KA1= 1 JA2 = A1 KA2= A1 JA3 = A2A1 KA3= A2A1 JA4 = A3A2A1 KA4= A3A2A1
and hence the logic diagram shown in Fig. 7-17.
Note that if we let JA1 = KA1 = 0 then none of the flip-flop will change its state,
and therefore we can use it to stop (i.e., to disable) the counter.
Sequential machine slide 33
![Page 34: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/34.jpg)
Design of a 4-bit synchronous down counter The state table
present
state (at time t)
next state
(at t+1) A4 A3 A2 A1
0 0 0 0 A4 A3 A2 A1
1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0
Sequential machine slide 34
![Page 35: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/35.jpg)
The excitation function for the four JK flip-flops
present state
(at time t)
next state
(at t+1)
JA1
KA1
JA2
KA2
JA3
KA3
JA4
KA4
A4 A3 A2 A1 0 0 0 0
A4 A3 A2 A1 1 1 1 1
1
X
1
X
1
X
1
X
0 0 0 1 0 0 0 0 X 1 0 X 0 X 0 X 0 0 1 0 0 0 0 1 1 X X 1 0 X 0 X 0 0 1 1 0 0 1 0 X 1 X 0 0 X 0 X 0 1 0 0 0 0 1 1 1 X 1 X X 1 0 X 0 1 0 1 0 1 0 0 X 1 0 X X 0 0 X 0 1 1 0 0 1 0 1 1 X X 1 X 0 0 X 0 1 1 1 0 1 1 0 X 1 X 0 X 0 0 X 1 0 0 0 0 1 1 1 1 X 1 X 1 X X 1 1 0 0 1 1 0 0 0 X 1 0 X 0 X X 0 1 0 1 0 1 0 0 1 1 X X 1 0 X X 0 1 0 1 1 1 0 1 0 X 1 X 0 0 X X 0 1 1 0 0 1 0 1 1 1 X 1 X X 1 X 0 1 1 0 1 1 1 0 0 X 1 0 X X 0 X 0 1 1 1 0 1 1 0 1 1 X X 1 X 0 X 0 1 1 1 1 1 1 1 0 X 1 X 0 X 0 X 0
Sequential machine slide 35
![Page 36: Analysis and Design of Sequential Circuits: Examples](https://reader031.fdocuments.us/reader031/viewer/2022020620/61e402ce666039385f230cdc/html5/thumbnails/36.jpg)
From the truth table we see that the desired inputs to the flip-flops can be
simplified to
JA1 = 1 KA1= 1 JA2 = A'1 KA2= A'1 JA3 = A'2A'1 KA3= A'2A'1 JA4 = A'3A'2A'1 KA4= A'3A'2A'1
This is reflected in the logic diagram shown in Fig. 7-18. Note that this design can
be directly translated into a T flip-flop implementation because the J input to every
flip-flop is identical to its K input.
Sequential machine slide 36