Question $1.$ Design a combinational circuit with $4$ inputs, A$3,$ A$2,$ A$1,$ A$0$; and three outputs, X$,$ Y$,$ Z$.$ The inputs represent a binary number in the range $[0.\mathrm{.}15],$ and the outputs represent characteristics of the numbers. Specifically, X should be true if the number is divisible by $3$; Y should be true if the number is prime; and Z should be true if the number is a power of $2.$ As an example, if the input is A $3$A $2$A $1$A $0=1100,$ this represents the number $12,$ which is divisible by $3,$ not prime, and not a power of $2$ so the outputs should be XYZ $=100.$ Recall that $0$ is divisible by any positive integer. $($a$).$ Implement the circuit with AND gates, OR gates, and NOT gates. You may use k$-$map for your design work, and inverted inputs on gates. $($b$).$ Implement the circuit using AND, OR$,$ NOT, and XOR gates. How much simpler is this design than the design in part $($a$)?$