Counters and Registers
445
C
Clk
FF-C
X (C)
1
C
Clock
B
Clk
FF-B
B
A
Clk
FF-A
A
X (C)
2
X (B)
1
X (B)
2
X (A)
1
X (A)
2
Figure 11.29 Counter circuit (example 11.8).
Table 11.12 Example 11.9.
Present state
Next state
Inputs
C
B
A
C
B
A
J A
K A
J B
K B
J C
K C
0
0
0
0
1
0
0
X
1
X
0
X
0
0
1
0
0
0
X
1
0
X
0
X
0
1
0
1
0
1
1
X
X
1
1
X
0
1
1
0
0
0
X
1
X
1
0
X
1
0
0
0
0
0
0
X
0
X
X
1
1
0
1
1
1
0
X
1
1
X
X
0
1
1
0
0
0
0
0
X
X
1
X
1
1
1
1
0
0
0
X
1
X
1
X
1
Solution
• The number of flip-flops required is three.
• Table 11.12 shows the desired circuit excitation table.
• The Karnaugh maps for J A , K A , J B , K B , J C and K C are shown in Figs 11.30(a) to (f) respectively
• The simplified Boolean expressions are as follows:
J A = BBC
(11.14)
K A = 1
(11.15)