The outputs of the two flip-flops $Q_{1}$ , $Q_{2}$ in the figure shown are initialized to 0, 0. The sequence generated at $Q_{1}$ upon application of clock signal is

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Solution

Initially $Q_{1}$ = $Q_{2}$ = 0
Truth table of JK:
J K $Q_{n}$
0 0 Previous state
0 1 0
1 0 1
1 1 ${¯ Q}_{n}$
Case - 1: 1st clock pulse
$Q_{1}$ = 0, ${¯ Q}_{1}$ = 1, $Q_{2}$ = 0, ${¯ Q}_{2}$ = 1
So, $J_{1}$ = 1, $K_{1}$ = 0 and $J_{2}$ = 0, $K_{2}$ = 1
So, $Q_{1}^{'}$ = 1, $Q_{2}^{'}$ = 0
Case - 2:
$Q_{1}$ =1, $Q_{2}$ = 0
${¯ Q}_{1}$ = 0, ${¯ Q}_{2}$ = 1
So, $J_{1}$ = 1, $J_{2}$ = 1
$K_{1}$ = 0, $K_{2}$ = 0
So, $Q_{1}^{'}$ = 1, $Q_{2}^{'}$ = 1
Case - 3:
$Q_{1}$ = 1, ${¯ Q}_{1}$ = 0, $Q_{2}$ = 1, ${¯ Q}_{2}$ = 0
$J_{1}$ = 0, $K_{1}$ = 1, $J_{2}$ = 1, $K_{2}$ = 0
$Q_{1}^{'}$ = 0, $Q_{2}^{'}$ = 1
So, the sequence will be 01100

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