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0011 1111 
   1101 0010    21010
   0110 1101    10910 
   0011 1111     6310

The carry bit of 1 indicates overflow.

Yet More Addition Practice

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