How do I create a 1-bit full adder that outputs a 2-bit sum?
So I looked up what constitutes a full adder and found its truth table.
Taken from wikipedia:

So you can see that if the adder has the correct output, your sum and carry bits are simply the 2 bit number you want.  So I guess all the full adder really does is add up to 3 binaries at a time instead of 2.