TASK:

$A_1{A}_0+B_1{B}_0+C_{in}.$

Design an adder circuit to sum two $2-$bit binary numbers by considering an initial carry in value.

a$.$ Draw the logic diagram.

b$.$ Draw the circuitry.

c$.$ Implement the circuit using logic gates and verify the circuit with following operations, and fill up the following table:

$\backslash$table$[[A_0,B_0,C_{in},S_0,A_1,B_1,S_1,C_{\text{o}\text{u}\text{t}}$