The quick summary is the 74181 looks at first like they picked 32 random functions but there's a rational explanation why it has functions like AB PLUS (A OR NOT B). And the gate arrangement makes sense once you realize it's all based on carry-lookahead.
You are the author? This is spectacular reading. Wonderful work, thank you. I have a question above about the transistor rendering in the second pic but I just now read your stackexchange link and have another question regarding this passage in the SE link:
"The first half of the chip's circuitry computes the four 1-bit sums of A with f(A,B). (Specifically it is creating the Generate and Propagate signals that are used for carry lookahead. This lets the 74181 work in parallel, rather than using a ripple carry.)."
Can you elaborate on "it is creating the Generate and Propagate signals.", I thought that the electrical pulse that drove combinatorial circuit was simply just the clock input on the chip. And that this was propagated to the whole chip instantaneously similar to a broadcast. Do I have this completely wrong?
"Generate" and "Propagate" are referring to the names of the signals in the first stage of a carry-lookahead adder ( https://en.wikipedia.org/wiki/Carry-lookahead_adder ). Generate is A AND B (AB), Propagate is A OR B (A + B). This is also where the AND and OR for the logic functionality comes from.
The '181 has no clock input, the outputs will change after some propagation delay whenever an input changes.
The quick summary is the 74181 looks at first like they picked 32 random functions but there's a rational explanation why it has functions like AB PLUS (A OR NOT B). And the gate arrangement makes sense once you realize it's all based on carry-lookahead.