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
Let the states be . From the circuit diagram, we can derive the next-state equations for the D flip-flops:
Substituting the equations:
This equation holds true if and only if . When , the condition must be satisfied. The states that satisfy are and .Therefore, there are 2 states that have a transition back to themselves (both occurring when the input is 0).
- , so
- , so
Substituting the equations:
1.
2.
From (1), we substitute for in (2):This equation holds true if and only if . When , the condition must be satisfied. The states that satisfy are and .Therefore, there are 2 states that have a transition back to themselves (both occurring when the input is 0).
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