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BTW check out a note I posted on the MHRD discussion.
https://gtm.steamproxy.vip/app/576030/discussions/0/4289188948007537743/
You might be interested.
It's chapter 2 of the book Leighton, F. Thomson. Introduction to Parallel Algorithms and Architectures. I can screenshot and send you some material via steam messages for starters since I wouldn't try and find or buy the book for that alone.
I happen to major in hardware but I don't remember anything specific about, but I guess with few clicks or looking it up on youtube you most definitely will find material about cla adders.
Basically there's hardware in row-cells doing the addition in parallel and calculating(basically predicting) whether you have a carry or not with 3 flags: G - S P (generate, stop, produce i think) and then there's an algorithm doing the calculation using binary trees. If you still wanna know about it I can refer you to some material :)
I'm not sure how the lookahead works. That level of math is a bit beyond me. But it does work.
This is the wiki address: https://en.wikipedia.org/wiki/Carry-lookahead_adder