Why is unsigned integer overflow defined behavior but signed integer overflow isn't?

Question

Unsigned integer overflow is well defined by both the C and C++ standards. For example, the C99 standard (§6.2.5/9) states

A computatio

Answer 1

Perhaps another reason for why unsigned arithmetic is defined is because unsigned numbers form integers modulo 2^n, where n is the width of the unsigned number. Unsigned numbers are simply integers represented using binary digits instead of decimal digits. Performing the standard operations in a modulus system is well understood.

The OP's quote refers to this fact, but also highlights the fact that there is only one, unambiguous, logical way to represent unsigned integers in binary. By contrast, Signed numbers are most often represented using two's complement but other choices are possible as described in the standard (section 6.2.6.2).

Two's complement representation allows certain operations to make more sense in binary format. E.g., incrementing negative numbers is the same that for positive numbers (expect under overflow conditions). Some operations at the machine level can be the same for signed and unsigned numbers. However, when interpreting the result of those operations, some cases don't make sense - positive and negative overflow. Furthermore, the overflow results differ depending on the underlying signed representation.