Implement the truth table given below using:

Input

X

Y

Z

F

$0$

$0$

$0$

$0$

$1$

$0$

$1$

$0$

$0$

$0$

$0$

X $($Don$\text{'}$t care$)$

$1$

$1$

$1$

$0$

$1$

$0$

$0$

$1$

$1$

$0$

$1$

$1$

$1$

$1$

$0$

X $($Don$\text{'}$t care$)$

$1$

$1$

Output

$1$

$1$

a$)$ A single $3-$to$-8$ Decoder and any needed logic gate. $[8$ points$]$

b$)$ A single $4-$to$-1$ Multiplexer and any needed logic gate. $[12$ points$]$