The addition of two 1-bit binary numbers looks like...
To let the addition of two 1-bit numbers be done by a logic circuit, you need to look at the truth table...
If you are only interested in a 1-bit response Q, you only need an XOR operation.
However, if you add up 1 and 1, the answer is more complicated. A 1 must be transferred to the next digit. This bit is called a Carry-Bit. As the output of a logic circuit, it is indicated with CO (Carry Out). The result of CO is realized with an AND operation.
This circuit is called a half adder.
But what do you need to add two 2-bit numbers...?