[Phillip] wanted to play with the C preprocessor. He decided to do that by creating a 4 bit full adder. We know this is pretty useless in everyday life, but it was a great learning experience.

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 ...

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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 ...