$3.$ Design of an Arbitrary Boolean Function with Constraints

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

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

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

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