32 bits.
Here is a problem with 4 bits:
1111 0111 1001 ---- 0000 Overflow was detected.
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
The electronic circuits of a computer can easily detect overflow 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.