$4.(20\text{'})$ Combinational Circuit Design: A circuit has four inputs and two outputs. The inputs A$3$:$0$

represent a number from $0$ to $15.$ Output $P$ should be TRUE if the number is prime $(0$ and $1$ are not

prime, but $2,3,5,$ and so on$,$ are prime$).$ The truth table of the circuit is shown in Figure $1.$

$.$ Based on the truth table, find the Boolean function of $P$ as function of $A[3],A[2],A[1],A[0]$

using SoP $($Sum$-$of$-$Product$)$ format.

$.$ Use Karnaugh map to find simplified Boolean equation of $P=?$

$.$ Sketch the gate$-$level implementation of the circuit.