Most processors nowadays work with 2's complement representation. That means that to build the negative value of a number n the formula
nneg = (2**WordSize - n) mod 2**WordSize
is used. For a 32-bit processor and your example value 15 that would be
nneg = 2**32 - 15 = 4 294 967 281 = 0xFFFF FFF1
Some older processors use One's Complement representation. For them the formula is
nneg = (2**WordSize-1 - n) mod 2**WordSize
which means that the value 0 has two representations namily 0x00000000 and 0xffffffff.