You can implement C in completely different ways. For example, I like that signed overflow is UB because it is trivial to catch it, while unsigned wraparound - while defined - leads to extremely difficult to find bugs.
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You can implement C in completely different ways. For example, I like that signed overflow is UB because it is trivial to catch it, while unsigned wraparound - while defined - leads to extremely difficult to find bugs.
There's 3 reasonable choices for what to do with unsigned overflow: wraparound, saturation, and trapping. Of those, I find wrapping behavior by far the most intuitive and useful.
Saturation breaks the successor relation S(x) != x. Sometimes you want that, but it's extremely situational and rarely do you want saturation precisely at the type max. Saturation is better served by functions in C.
Trapping is fine conceptually, but it means all your arithmetic operations can now error. That's a severe ergonomic issue, isn't particularly well defined for many systems, and introduces a bunch of thorny issues with optimizations. Again, better as functions in C.
On the other hand, wrapping is the mathematical basis for CRCs, Error correcting codes, cryptography, bitwise math, and more. There's no wasted bits, it's the natural implementation in hardware, it's familiar behavior to students from a young age as "clock arithmetic", compilers can easily insert debug mode checks for it (the way rust does when you forget to use Wrapping<T>), etc.
It's obviously not perfect either, as it has the same problem of all fixed size representations in diverging from infinite math people are actually trying to do, but I don't think the alternatives would be better.
Addition of two 1-bit numbers produces a 1-bit number, which is simple and fundamental enough that we call it XOR. If you take that N-bit adder and drop the final carry (a.k.a use a couple XORs instead of the full adder), you get wrapping addition. It's a pretty natural implementation, especially for fixed width circuits where a carry flag to hold the "Nth+1" bit may not exist, like RISC-V.