$(10\%,5\%$ for each$)$ A sequential circuit has two inputs and two outputs. The inputs $($ X $1$ and X $2)$ represent a $2-$bit binary number, N $.$ If the present value of N plus the previous value of N is greater than $2,$ then the Z $1$ is $1.$ If the present value of N times the previous value of N is greater than $2,$ then Z $2$ is $1.$ Otherwise, Z $1$ and Z $2$ are $0.$ When the first pair of inputs is received, use $0$ as the previous value of N $.$

$($a$)$ Find a Mealy state table for the circuit.

$($b$)$ Find a Moore state table for the circuit.