Show the truth table for a two$-$bit binary adder$-$that is a circuit with

Four inputs, $a_1,a_0,b_1,b_0$

$a_1{a}_0$ and $b_1{b}_0$ represent two $2-$bit unsigned binary integers

Three outputs, $c_{\text{o}\text{u}\text{t}},s_1$ and $s_0.$

$c_{\text{o}\text{u}\text{t}}$ represents a carry signal from the sum of the two $2-$bit integers and

$s_1{s}_0$ represents the $2-$bit unsigned binary sum of the two $2-$bit integers.

For credit, ensure you order your input $a_1{a}_0{b}_1{b}_0$ and

Your output $c_{\text{o}\text{u}\text{t}}{s}_1{s}_0.$

Notice there is no $c_{in}.$ You're welcome! Why is this a very good thing from your point of view?

$(1\mathrm{.}0$ Points$)$