1) You/we cannot draw a circuit if we don't know what we are designing. You figure out the logic first then you draw the circuit.
2) This is your homework, not ours. You have to learn how to do things on your own.
An adder is just another combinatorial circuit that can be realized with a selection of standard logic gates. Google "Half-Adder" and "Full-Adder". The difference has to do with handling the carry. This is your homework - attack it with relish! Do you really need a professor to lead you around by the ring?