Design a circuit that has a $3-$bit binary input $B2,B1,B0,$ where $B2$ is $MS{B}^{**}$ and $B0$ is $LS{B}^{****}.$ A

single output $Z$ is dictated as follows:

$Z=0,$ even numbers

$Z=1,$ odd numbers $1,3,5,7$

a$)$ Create the truth table for the above requirements.

b$)$ Construct the Sum of Product equation.

c$)$ Draw the circuit of the equation.