a$)$ Design a combinational circuit with three inputs and one output. The output is $1$ when the sum of digits is odd.

Note: Derive the logical expression by constructing truth table and arrive at the logic circuit diagram

b$)$ Simplify the following Boolean expression and mention the Boolean law used.

$A^{\text{'}}BC{D}^{\text{'}}+BC{D}^{\text{'}}+B{C}^{\text{'}}{D}^{\text{'}}+B{C}^{\text{'}}D$