Question

Consider a finite state machine (FSM) with one input \(X\) and one output \(f\), represented by the given state transition table. The minimum number of states required to realize this FSM is __________ (Answer in integer).

 

Hint:

To minimize FSM states, group states that have identical outputs and transitions. This helps in reducing the complexity of the state machine.

Answer 1

To find the minimum number of states for the FSM, we need to minimize the state diagram based on the state transitions and outputs.

The given state transition table is:

Step 1: Identify the equivalence classes of states.
We need to classify the states based on their transitions and outputs. After inspecting the table, we see that states A, B, and H form a group due to the same transitions and outputs, while other states can be similarly grouped.

Step 2: Minimize the state diagram.
By merging the equivalent states, we reduce the total number of states from 8 to 5. These are the minimized states:

A, B, H form one group.
F, C form another group.
D, G, E form another group.

Thus, the minimum number of states required is 5.