If the integer representation used is "0 through 4,294,967,295 (2^32 − 1)", so does this mean the register cannot handle negative numbers?
The contents of a register don't have any inherent semantics.
Some instructions might assume certain semantics. For example, the x86 ADD instruction assumes that the registers represent integers, either unsigned or signed using two's complement. There are signed and unsigned versions in the x86 architecture for the multiplication instructions. Another unlikely place in which sign makes a difference is promotion instruction, in which a smaller register is assigned to a larger register – you want either zero extension (in the unsigned case) or sign extension (in the signed case, assuming two's complement).
What this all means is that certain the instruct set favors some interpretations by having instructions that assume them, but beyond that, the interpretation of the data stored in a register is completely up to the user. Moreover, in x86 at least, the same register can be used for both signed and unsigned operations. The register doesn't &quot;know&quot; which type of data it stores – it is completely up to the programmer. (One could imagine different architectures with different conventions.)