Q$8)$ A sequential circuit has a single input $x$ and a single output $y.$ When the sequence $"110"$ occurs at the input, the output becomes $1$ and remains $1$ until the sequence $"110"$ occurs again in which case the output returns to $0.$ The output remains $0$ until $"110"$ occurs a third time, etc. Initially the output is $0.$

$($a$)$ Draw the corresponding state diagram for a Moore machine.

$($b$)$ List the state table and design the circuit using $D$ flip$-$flops.

$($c$)$ Draw the logic diagram of the circuit.