Question

For the sequential circuit using three J-K flip flops and one AND gate shown below, output of the circuit becomes 1 after every N clock cycles. The value of N is______.

Answer 1

Let initially output is 1

$(J_0=1,K_0=1,J_1={\overline{Q}}_2,K_1=1,J_2=Q_1,K_2=1)$
Then

CLK	$Q_0$	$Q_1$	$Q_2$	$Q_0^{+}$	$Q_1^{+}$	$Q_2^{+}$	$J_{+}0$	$K_0$	$J_1$	$K_1$	$J_2$\	$K_2$	Z
Initially	0	0	0										1
1	1	1	0	1	1	0	1	1	1	1	0	1	0
2	0	0	1	0	0	1	1	1	1	1	1	1	0
3	1	0	0	1	0	0	1	1	0	1	0	1	0
4	0	1	0	0	1	0	1	1	1	1	0	1	0
5	1	0	1	1	0	1	1	1	1	1	1	1	0
6	0	0	0	0	0	0	1	1	0	1	0	1	1

It is mod - 6 counter, so output Z will be 1 after every $6^{th}$ clock pulse.