P$5(20$ points$)$ Design and implement a Moore finite state machine $($FSM$)$ that detects the sequence $"1010"$ in a $1-$bit serial input stream without overlap. The output is $1$ if the sequence is detected and $0$ otherwise. In your solution, include the following:

a$)(5$ points$)$ Draw the state diagram for the FSM$.$

b$)(5$ points$)$ Write the state table and the state$-$assigned table.

c$)(5$ points$)$ Derive the logical expressions for the next state and output variables.

d$)(5$ points$)$ Draw the circuit diagram using $\backslash ($ D $\backslash )$ flip$-$flops based on the derived expressions.