Design a Moore machine that has a single input $x$ and a single

output $Y$ that works as follows.

Machine is always in one of the two modes: free and

blocked.

If machine is free and $x=0,$ then in the next three CLKs$,$ it

will emit sequence $101$ as output. It will be blocked until

the entire sequence is emitted.

If machine is free and $x=1,$ then in the next three CLKs$,$ it

will emit sequence $010$ as output. It will be blocked until

the entire sequence is emitted.

Inputs that arrive when the machine is blocked do not

affect the output.

An example input$-$output sequence is given below:

$($i$)$ Draw the state diagram with minimum number of states.

$15pts$

$($ii$)$ What is the minimum number of flip$-$flops needed to

implement this circuit? Will there be any unused flip$-$flop

states? If so$,$ how many? $[5$ pts$]$