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.
Which one of the following statements is correct?
Correct answer
(C) Transitions from State C are ambiguously defined.
Solution
A state transition is ambiguously defined if for a given input, there is more than one possible next state (overlap) or no defined next state (incomplete).
- State B: Transitions are , , and . These are mutually exclusive and their sum is . It is unambiguous.
- State C: Transitions are (self-loop), (to A), and (to B). If , both transitions to A and B are satisfied, creating an overlap. Also, if , no transition is defined. Thus, State C is ambiguously defined.
- State A: Depending on interpretation of shorthand, it might have overlaps (e.g., and ), but State C is definitively ambiguous due to both overlap and incompleteness.
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