Question $2$: $[25$ points $]$

Consider the following truth table which represents the operation of some combinational logic

circuit:

Table $1$: Truth Table for some "mystery combinational logic circuit"

$($a$)$ Draw the digital logic diagram which corresponds to the above table $($ the inputs to the circuit

are $I{N}_1$ and $I{N}_0$ and the outputs of the circuit are $OU{T}_1$ and $OU{T}_0.).$ Make use of ONLY the fol$-$

lowing types of logic gates in your diagram: inverters, $2-$input AND gates, $2-$input OR gates.

Your may use as many gates of each type as necessary. Identify clearly in your diagram the inputs

and the outputs.

Hint: Here is the hardware for the output $OU{T}_0($it is simply a wire$)$ :

$I{N}_0$

$OU{T}_0$

$($b$)$ Does the $2-$bit parallel adder shown in Figure $1$ give the same output as specified by the

above truth table? can you please answer the entire question as well as the blank and drawing the circuit with explanation thanks