GATE CS 2018 Set 1 — Question 32
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Digital Logic → Sequential Circuits → Flip-Flops (JK, T, D)
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Question
Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops.
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 _____.
Correct answer
2 to 2
Solution
In the circuit, the input
in drives the D input of the first flip-flop, the output of the first flip-flop drives the D input of the second, and is out. Both flip-flops share the clock, so this is a 2-bit shift register:Take the state as . A state has a self-loop if, for some value of in, , i.e.The second condition does not depend on the input, so only states with can loop:- : with
inthe next state is — self-loop. - : with
inthe next state is — self-loop. - and : the next equals the current , so they always move to a different state.
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