Overflow Detection

Here is an addition problem using 4-bit operands:

1111
 0111
 1001 
 0000
 
Overflow happened

Two four-bit numbers are added, but the sum does not fit in four bits. If we were using five bits the sum would be 1 0000. But with four bits there is no room for the left-most "1". Because the carry out from the most significant column of the sum is "1", the 4-bit result is not valid. The column is called the most significant column because it corresponds to the highest power of two. The bits in the leftmost columns are called the most significant bits or the high-order bits.

The electronic circuits of a processor can easily detect overflow of unsigned binary addition by checking if the carry-out of the leftmost column is a zero or a one. A program might branch to an error handling routine when overflow is detected.