GATE 2017 CS – Question 43
Consider a combination of T and D flip-flops connected as shown below. The output of the D flip-flop is connected to the input of the T flip-flop and the output of the T flip-flop is connected to the input of the D flip-flop.
[Figure: A T flip-flop with output $Q_1$ and a D flip-flop with output $Q_0$, both on the same clock. The D flip-flop output $Q_0$ goes to the T input, and the T flip-flop output $Q_1$ goes to the D input.]
Initially, both $Q_0$ and $Q_1$ are set to 1 (before the 1st clock cycle). The outputs
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Correct answer: (B) $Q_1 Q_0$ after the 3rd cycle are 11 and after the 4th cycle are 01 respectively
Explanation
At each clock edge $Q_1$ toggles if $Q_0 = 1$, so $Q_1^{+} = Q_1 \oplus Q_0$, and $Q_0$ takes the old value of $Q_1$. Starting from $(Q_1, Q_0) = (1, 1)$: after cycle 1 it is $(0, 1)$, after cycle 2 it is $(1, 0)$, after cycle 3 it is $(1, 1)$, and after cycle 4 it is $(0, 1)$. So the outputs are 11 after the 3rd cycle and 01 after the 4th.