Design a sequential circuit with one input $($X$)$ and two outputs $($Y$,$ Z$).$ The $2-$bit output YZ represents the cumulative count of adjacent $1$s encountered in the input sequence so far. For example:

The input sequence $"0110"$ results in $1$ adjacent $1.$

The input sequence $"01110"$ results in $2$ adjacent $1$s$.$

The input sequence $"0110111"$ results in $3$ adjacent $1$s$.$

When the count of adjacent $1$s reaches $4,$ the system resets to its initial state. Draw a Moore state diagram for this circuit design.

$(10$ points$)$

Note:

Assign meaningful descriptions to each state.

Perform state reduction if necessary.