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It is always true if we allow for correct width. The issue of 8 bit width representing numbers from 0~127 and -1 to -128 is separate.
The puzzle still stands:
- => + should reverse + => - naturally
hence for - => + subtract 1 then invert (by definition)
but how come the same rule apply to both conversions as well.
i.e. [invert add 1] in either case.
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If you search Wikipedia for "two's complement" there is an explanation, but rather complex.
For me, when you start with a positive number and complement the objective is to find the distance from zero in the negative direction so when you complement 0 "adding 1" has the effect of reducing the magnitude so that 0 is still zero, but the magnitude of all negative numbers appears to be offset toward 0. When you complement the negative number you have to add 1 to adjust the magnitude to get the correct distance from 0 in the positive direction. Therefore the maximum negative number 1.000 ... 0 is farther away from 0 than the maximum positive number and cannot be converted.
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