Modern Computer Architecture and Organization, by Jim Ledin. Published by Packt Publishing.
Consider the addition of two signed 8-bit numbers (that is, numbers in the range -128 to +127) where one operand is positive and the other is negative. Is there any pair of 8-bit numbers of different signs that, when added together, will exceed the range -128 to +127? This would constitute a signed overflow. Note: We’re only looking at addition here because, as we’ve seen, subtraction in the 6502 architecture is the same as addition with the right operand’s bits inverted.
The range of the positive (or nonnegative) numbers is 0 to 127. The range of negative numbers is -128 to -1. It is only necessary to consider the extremes of each of these ranges to cover all possibilities.
| Sum | Result |
|---|---|
| 0 + -128 | -128 |
| 127 + -128 | -1 |
| 0 + -1 | -1 |
| 127 + -1 | 126 |
There is no pair of 8-bit numbers of different signs that, when added together, exceeds the range -128 to +127.