GATE CS 2025 Set 1 — Question 59
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Digital Logic → Sequential Circuits → State Minimization
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Question
Consider a finite state machine (FSM) with one input and one output , represented by the given state transition table. The minimum number of states required to realize this FSM is ________. (Answer in integer)
Correct answer
5 to 5
Solution
We use the state reduction method by partitioning states based on their outputs and next-state behavior.
1.Initial Partition () based on outputs :
- with outputs
- with outputs
- with outputs
- with outputs
- For :
- A: next states are (F, B)
- B: next states are (D, C)
- C: next states are (F, E)
- E: next states are (D, C)
- For :
- D: next states are (G, A)
- H: next states are (G, A)
3.Final Partition: .
Checking for further refinement shows that no more splits are possible. The minimum number of states is .Continue learning with Success Tracker
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