$2.$ A sequential circuit has two inputs $\backslash ($ X $\backslash )$ and $\backslash ($ Y $\backslash )$ and one output $\backslash ($ Z $\backslash ).$

$-$ If no $1\text{'}$s have been received on $\backslash ($ X $\backslash ),$ then $\backslash ($ Z $\backslash )$ is whatever $\backslash ($ Y $\backslash )$ is$.$

$-$ If one $1$ has been received on $\backslash ($ X $\backslash ),$ then $\backslash ($ Z $\backslash )$ is $1$ if the number of $1\text{'}$s received on $\backslash ($ Y $\backslash )$ is a multiple of $2,$ and $0$ otherwise.

$-$ If two or more $1\text{'}$s have been received on $\backslash ($ X $\backslash ),$ then $\backslash ($ Z $\backslash )$ is the opposite of whatever $\backslash ($ Y $\backslash )$ is$.$

For example

$```$

X:$00010001011$

Y:$01001110110$

Z:$01001011001$

$*$ no $1\text{'}$s on X: Z is whatever Y is$.$

$-$ one $1$ on X$,$ two $1\text{'}$s on Y: two is a multiple of $2$

$-$ one $1$ on X$,$ four $1\text{'}$s on Y: four is a multiple of $2$

$....$ two or more $1\text{'}$s on X: Z is the opposite of Y$.$

$```$

$($a$)$ Pick one or the other, Moore or Mealy. Draw a state diagram.

$($b$)$ Then assign states to the bits of flip$-$flops.

$($c$)$ Then, design the combinational logic to compute the next state.

$($d$)$ Then, design the combinational logic to compute the output.

DRAW THE STATE DIAGRAM