Simplified half adder. A is top switch. B is a pulse input. CIN is bottom switch. Sum is top LED. Carry is bottom LED.
I hate the fact that I have to use double throw switch for input otherwise the circuit does not work as it should.
Due to current limitations of work space a full adder may be possible but either no inputs or outputs. If they ever increase the workspace or allow circuits to be made into an IC then even more would be possible.