11 1101 0010 21010 0110 1101 10910 0011 1111 6310
The carry bit of 1 indicates overflow.
The correct application of the "Binary Addition Algorithm" sometimes gives incorrect results (because of overflow). With paper-and-pencil arithmetic, overflow is not a problem because you can use as many columns as needed.
|Correct Unsigned Binary Addition|
When the "Binary Addition Algorithm" is used with unsigned binary integer representation:
The result is CORRECT only if the CARRY OUT of the high order column is ZERO.
But digital computers use fixed bit-lengths for integers, so overflow is possible. For instance some processors represent integers in 8, 16, or 32 bits. When 8-bit operands are added, overflow is certainly possible. Our MIPS processor uses 32-bit integers, but even with them, overflow is possible.
Compute the following sum using 8 bits:
0000 0001 1111 1111