In decimal, adding 10 to a positive number leaves the units digit unchanged, as does subtracting 10 from a negative number. This is also true when adding or subtracting integer multiples of 10, so long as the result is of the same sign as the initial number. However, this is not generally true when crossing the zero boundary: $7 - 10 = -3$, since the standard representation of a negative number (e.g. -3) mirrors the number line at 0.
A related statement is that the units digit of a positive number is equal to the number modulo 10, and the units digit of a negative number is equivalent to the absolute value of 10 less than the number modulo 10:
- 13: $13 \equiv 3 \mod 10$
- -13: $-13 \equiv \lvert(-13 \mod 10) - 10\rvert$
Are there any representations of negative numbers that continue the units digit pattern when crossing from the positive numbers to the negative numbers? For instance, -13 would be represented as $(-10) + 3$. I would imagine there might be contexts where this might be more convenient.
I might just not know what to search for, but the one related concept I have been able to find is the offset binary method for signed number representation in computing. However, that appears to only shift the problem such that 0 represents a number smaller than zero.
