How can you tell whether a value fits in a register of a given size?

Check whether the number lies within that width's representable range — and remember the signed and unsigned ranges differ.

Each width holds a fixed span of values; overflow is what happens when you exceed it.

The subtle trap in x86-64 is that immediate operands in instructions are 32-bit sign-extended, which interacts badly with large unsigned constants:

mov $0x7FFFFFFF, %eax   # fine — fits in 32-bit signed
mov $0x80000000, %eax   # OK into %eax, but as a 64-bit immediate it
                        # would sign-extend to 0xFFFFFFFF80000000!
movabs $0x80000000, %rax  # use movabs for an exact 64-bit immediate

Tip: movl into a 32-bit register zero-extends the result, but an immediate encoded in an instruction is sign-extended — two different rules that are easy to confuse.

Go deeper:

• Two's complement (Wikipedia) — the signed and unsigned representable ranges per bit-width.