We’ll use maps to design a full adder with more rigor than used designing the half adder. A full adder has the same two X and Y inputs but also an input carry, Cin, sent from the previous stage.

The article has a lot of detail about both the design and build as well as the theory behind the adder. Other articles on binary adders on the site include this one which uses bigger relays ...

In addition, the BA22 was designed to minimize code ... The Multiply Adder IP performs a multiplication of two operands and adds (or subtracts) the full-precision product to a third operand.The ...