Design a $4-$variable Boolean function G$($W$,$ X$,$ Y$,$ Z$)$ such that: G $=1$ when the binary representation of W XY Z is a prime number, and $0$ otherwise.

$($a$)$ List the prime numbers represented in binary by four variables W$,$ X$,$ Y$,$ Z$.$

$($b$)$ Determine the minimal SOP $($Sum of Products$)$ form of G using a Karnaugh map.

$($c$)$ Convert G into a circuit using a combination of AND, OR$,$ and NOT gates.