The first "addition" example above is called a half-adder.

Basic understanding of digital logic design - gates, half-adder.

Fig. 1 illustrates the configuration of a half-adder using a crossbar tile, as taught by Snider, with the nodes identifying junctions of the crossbar tile configured as low-resistance states.

By setting different logic inputs A, NOT A, B, and NOT B to different row wires this configuration produces the sum and carry outputs typical for a half-adder.