a$)$ Create a combinational circuit capable of subtracting a constant value of $\text{'}2\text{'}$ from a $3-$bit

binary number represented in $2\text{'}$s complement form. In order to support your design,

include a truth table, describe the Boolean expression simplification technique used, and

provide a logic circuit diagram.

b$)$ Minimize the following using K$-$map technique.$|$

F$($W$,$x$,$Y$,$Z$)=\backslash$Sigma m$(1,4,6,9,10,14,15)+$d$(2,8)$