Casting Signed to Unsigned in C

Someone had asked earlier if assigning from signed to unsigned just took the absolute value. The answer, generally speaking, is, "no, it does weird things".

In C, C++, and Go (and probably a pile of other languages), converting from signed to unsigned basically does the following, according to spec:

while (number < 0) {
    number += MAX_UNSIGNED_INT + 1
}

This looks really weird (WHY would they do this??!!), but what's actually happening is a little bit simpler.

Deep down, the computer represents numbers as bits in sequential bytes. Using something called 2's complement representation, signed numbers are stored like so (using a 4-bit number for the sake of example simplicity--but it could be 64 bits, or whatever):

Signed:

binary 0001 = decimal  1    signed
binary 0000 = decimal  0
binary 1111 = decimal -1
binary 1110 = decimal -2

But compare that to how unsigned numbers are stored:

binary 0001 = decimal  1    unsigned
binary 0000 = decimal  0
binary 1111 = decimal 15 
binary 1110 = decimal 14

The bit pattern for 15 is the same as the bit pattern for -1. When you convert from signed to unsigned, all it does is change how it's interprets the exact same bit pattern.

binary 1111 == signed decimal -1 == unsigned decimal 15

That means on a 4-bit machine, converting -1 to unsigned gives you 15.

On a 32-bit machine, converting -1 to unsigned gives 4294967295, which is binary 11111111111111111111111111111111 in both cases.