Question $3$: $(10$ points$)$ Derive a Mealy state diagram, perform state assignment, and then synthesize expressions for the next$-$state and output signals for the following problem. A sequential circuit has two inputs, $w_1$ and $w_2,$ and an output, $z.$ Its function is to compare the input sequences on the two inputs. If $w_1=w_2$ during any four consecutive clock cycles, the circuit produces $z=1$; otherwise, $z=0.$ For example

$w_1$:$0110111000110$

$w_2$:$1110101000111$

$z$:$0000100001110$