Consider the sequential circuit shown in the figure, where both flip-flops…
2018
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 _____.
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Correct answer: 2
Answer: 2
Explanation: Let Q1 be the output of the first flip-flop and Q2 be the output of the second flip-flop. On a clock edge the next state is Q1(next) = in and Q2(next) = Q1.
A state (Q1,Q2) has a transition back to itself for some input if (in,Q1) = (Q1,Q2). That gives the conditions in = Q1 and Q1 = Q2.
States with Q1 = Q2 are 00 and 11; these satisfy the condition and therefore have self-transitions (choose in = 0 for state 00, in = 1 for state 11).
States 01 and 10 do not satisfy Q1 = Q2, so no input can produce a transition back to the same state.
Therefore the number of states that have a transition back to themselves for some input is 2.
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