GATE EC 2016 Set 2 — Question 54
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Digital Circuits → Sequential Logic → FSM (Mealy & Moore)
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Question
The state transition diagram for a finite state machine with states A, B and C, and binary inputs X, Y and Z, is shown in the figure.
The transitions in the diagram are: from A, stay in A if or if ; go to B if ; go to C if . From B, stay in B if ; go to A if ; go to C if . From C, stay in C if ; go to A if ; go to B if .Which one of the following statements is correct?
Correct answer
(C) Transitions from State C are ambiguously defined.
Solution
A state's transitions are ambiguous if some input combination satisfies the conditions of two arcs leading to different next states.State A: conditions (to A), (to A), (to B), (to C). The only overlap is between the two self-loops (), and both lead to A, so there is no conflict. Not ambiguous.State B: conditions (to B), (to A), (to C). These three are mutually exclusive and cover all inputs. Not ambiguous.State C: conditions (to C), (to A), (to B). For both the arc to A and the arc to B are satisfied, so the next state is not uniquely defined. (In addition, satisfies no arc.) Ambiguous.Hence (A), (B) and (D) are false and (C) is correct.Answer: (C)
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