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As the authors mentioned, this circuit is 1 modulo 3 counter. Here we have K_0 =

ID: 3868755 • Letter: A

Question

As the authors mentioned, this circuit is 1 modulo 3 counter. Here we have K_0 = K_1 = 1. Consider the 3 other variations of this example with (a) K_0 = K_1 = 0 (b) K_0 = 1, K_1 = 0 (c) K_0 = 0, K_1 = 1 Derive a table similar to Figure 5.72 for each of these 3 variations. In Figure 5.72 we see patterns repeat as 00, 01, 10,00, 01 and hence we observe the counting sequence 0, 1, 2, 0, 1 and so on: and it is concluded that this circuit is a modulo-3 counter. For these three variations, derive a table of 5 entries similar to Figure 5.72 (with the First column as Clear, t_1, t_2, t_3, and t_4).

Explanation / Answer

a) for k0 = k1 = 0

Time Interval

FF0

FF1

J0

K0

Q0

J1

K1

Q1

Clear

1

0

1

1

0

1

t1

0

0

0

0

0

0

t2

1

0

1

1

0

1

t3

0

0

0

0

0

0

t4

1

0

1

1

0

1

We see patterns repeat as 11 , 00 ,11,00 , 11 and hence we observe the counting sequence 3 ,0,3 ,0 ,3 and so on.

b) For K0 = 1 , K1=0

Time Interval

FF0

FF1

J0

K0

Q0

J1

K1

Q1

Clear

1

1

0

0

0

0

t1

1

1

1

1

0

1

t2

0

1

0

0

0

0

t3

1

1

1

1

0

1

t4

0

1

0

0

0

0

We see patterns repeat as 00,11 , 00 ,11, 00 and hence we observe the counting sequence 0,3 ,0,3,0 and so on.

c) For K0=0 and K1=1

Time Interval

FF0

FF1

J0

K0

Q0

J1

K1

Q1

Clear

0

0

0

0

1

0

t1

1

0

1

1

1

1

t2

0

0

0

0

1

0

t3

1

0

1

1

1

1

t4

0

0

0

0

1

0

We see patterns repeat as 00 , 11, 00, 11, 00 and hence we observe the counting sequence 0,3 ,0,3,0 and so on.

Time Interval

FF0

FF1

J0

K0

Q0

J1

K1

Q1

Clear

1

0

1

1

0

1

t1

0

0

0

0

0

0

t2

1

0

1

1

0

1

t3

0

0

0

0

0

0

t4

1

0

1

1

0

1