Problem $7$: Find the prime numbers.

Design a logic circuit that tests if a $4-$bit binary number is a prime number in the decimal format. Assume that the input is represented by the signals $a,b,c,$ and $d,a$ is the MSB and $d$ is the LSB$,$ the output for the circuit is represented by $f,$YES$=1,NO=0$ for the prime numbers.

$($a$)$ Draw the Truth Table for the function.

$($b$)$ Implement the logic function only use the $8-$to$-1$ multiplexer and basic gates such as AND, OR and NOT, label all inputs and pins.

$($c$)$ Draw the Truth Table in this page. This time implement the logic function only use the $4-$to$-1$ multiplexer and basic gates such as AND, OR and NOT, label all inputs and pins.