Question

Q- Draw a state diagram for Moore FSM which can detect either of the two sequences 01X (overlapping).

This question is from the topic "Digital System Design using FPGA"

Answer 1

According to the Moore model, the output is represented with the state and input are shown on arrows.

Example - The state shown here is just for understanding of Moore model.

In the question, there are two sequences to be detected i.e. 010 and 011. The output will be 1 when either of the sequences is detected.

The output will be having different states as shown below and state diagram explanations are after that,

The state 'D' gets divided into states D₀ and D₁ , as the sequence will be detected differently for different input at previous state.

At state A,

At state B, The sequence detected till now is 0, after that, it can get 0 or 1 as input. If the input is 0 it can again detect the sequence using 2 more states. So for 0 as input, it will remain at the same state B.

At state C, the sequence detected until this state is 01. If the input at state C is 0 it will go to state D₀ and if the input is 1 it will go to state D₁.

As state D is divided into states D₀ and D₁ we need to check for them as this is overlapping type so the sequence can be detected again using the previous states.

The final state diagram is shown below for the given (overlapping) sequence.