The vintage 74181 ALU chip: how it works and why it’s so strange (2017)

It turns out that there is a rational system behind the operation set: they are simply the 16 logic functions added to A along with the carry-in.2 That is, the arithmetic functions are: A PLUS f(A,B) PLUS carry-in. Then each bit of A PLUS f(A,B) will always be 1 except in the case where A is 0 and B is 1, so the result of the sum is A OR NOT B. Even though you’re doing addition, the result is a logical function since no carry can be generated. In the 74181, the four f values are supplied directly by the four Select (S pin) values, resulting in the following table:6

The chip uses the logic block below (repeated four times) to compute P and G for each bit.

Source: www.righto.com