GATE 2018 CS – Question 32
Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops (a serial chain with input `in` and output `out`).
The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of "in" is ________.
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Correct answer: 2
Explanation
The circuit is a 2-bit shift register, so the next state is (in, $Q_1$). A state $(Q_1Q_2)$ stays the same only if $in=Q_1$ and $Q_1=Q_2$. That means only $00$ (with $in=0$) and $11$ (with $in=1$), which is 2 states.