Please show the moore graph, state table and $k-$maps $if$ needed with their equations Thank you!.

A sequential circuit has one input $(x)$ and one output $(Y).x$ represents a string of bits, which is input least

significant bit first. The circuit sets $Y=1$ when it detects the pattern $\text{'}101\text{'}$ in input $x($rightmost digit is the

least significant bit$).$ It keeps $Y=1$ until the end of the next occurrence of $\text{'}101\text{'}$ in the input $x.$ No

overlapping in $x($i$.$e$.10101$ is not treated as two $101$ sequences$).$ Example:

$x=00000010100000010100000010111111010000$

$Y=00000000011111111100000000011111110000$

$($a$)$ Derive a Moore state graph and state table.

$($b$)$ Try to choose a good state assignment. Explain why you have used that assignment.

pl$($c$)$ Realize the circuit using D flip$-$flops and NOR gates.