Question:

Design a Mealy machine that detects the input pattern, $110,$ and outputs $1$ upon detecting correctly. The machine should then reset and go to the initial state to get a new sequence. The machine is non$-$overlapping, which means that each successfully detected sequence is independent of other sequences.

a$)$ Draw the state diagram of the machine assuming the states, S $0($Initial$),$ Correct Detection$),$ S$2(2{?}^{nd}$ Correct Detection$),$ S$3(3{?}^{rd}$ Correct Detection$),$ S$4($Reset$).$

b$)$ Derive the state table from the state diagram.

c$)$ State whether the reduction of the state table is possible. If possible, reduce the state table and redraw both the reduced state table and reduced state diagram.

d$)$ Find the characteristic equations for Next States and Output.

e$)$ Implement the logic using D Flip Flops.

Hint: The reset state will automatically take the control to the Initial State after $500s.$