Twos complement is simply=1s complement+1. But there are various proofs, derivations that can be studied in twos complement that leads to faster arithmetic hardware implementation in computer engineering.

For example: Robertson algorithm for multiplication, Booth's algorithm etc.

I am wondering if there are mathematics books(name pls) that cover these derivations as a form of exercises or examples.

Comments (1)

mindcrime · 54m ago

Maybe something in Hacker's Delight[1]? Or Swartzlander's Computer Arithmetic[2] series? There's probably also some coverage somewhere in the Knuth's The Art of Computer Programming, but no idea which volume off-hand.

And if you really want to go down a rabbit hole, there's the Computer Arithmetic[3] conference[4] proceedings[5].

[1]: https://en.wikipedia.org/wiki/Hacker%27s_Delight

[2]: https://www.amazon.com/Computer-Arithmetic-Volumes-Earl-Swar...

[3]: https://en.wikipedia.org/wiki/Computer_arithmetic

[4]: https://en.wikipedia.org/wiki/ARITH_Symposium_on_Computer_Ar...

[5]: https://www.acsel-lab.com/arithmetic/

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