So far, we have studied the representation of negative numbers using ten’s complement. In a computer, we prefer using base two rather than base ten. Luckily, the exact method described in the previous section works just as well for base two. For an n-bit adder (n is usually 32 or 64), we can represent positive numbers with a leftmost digit of 0, which gives values between 0 and 2(n-1) - 1, and negative numbers with a leftmost digit of 1, which gives values between -2(n - 1) and -1.

The exact same rule for overflow and underflow detection works. If, when adding two positive numbers, we get a result that looks negative (i.e. with its leftmost bit 1), then we have an overflow. Similarly, if, when adding two negative numbers, we get a result that looks positive (i.e. with its leftmost bit 0), then we have an underflow.