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 tae uved ABCD'$+$BCD$\text{'}+$BC$\text{'}$D$\text{'}+$BC$\text{'}$D