> Both signed and unsigned arithmetic are using finite fields, This is not correct. They are rings with some additional (not mathematically standard) operation

> Both signed and unsigned arithmetic are using finite fields, This is not correct. They are rings with some additional (not mathematically standard) operations thrown in. 'Finite field' means something very specific, and quite different. https://en.wikipedia.org/wiki/Finite_field https://en.wikipedia.org/wiki/Finite_field Computer integer arithmetic hardware can be used to implement finite field arithmetic, but even the 2^n case takes quite a bit of trickery. https://en.wikipedia.org/wiki/Finite_field_arithmetic https://en.wikipedia.org/wiki/Finite_field_arithmetic