0011 1111
11
1101 0010 21010
0110 1101 10910
0011 1111 6310
The carry bit of 1 indicates overflow (for 8-bit unsigned addition).
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 |
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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.
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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 then, overflow is possible.
For interesting videos showing the consequences of overflow, google Ariane flight V88.
Compute the following sum using 8 bits:
0000 0001 1111 1111