Instead of a negative sign, allow some digits to represent negative numbers. In base 10, define $a=-4, \; b=-3, \; c=-2, \; d=-1$:
$\cdots$ -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 $\cdots$ $\to$ $\cdots$ d4 d5 a b c d 0 1 2 3 4 5 1a 1b 1c 1d 10 11 $\cdots$
Any number expressible with just the positive digits is the same: $10\to10$, $5213\to5213$. Addition, multiplication, other operations are sensible, it works for any base higher than binary. A number is negative if the first digit is one of the negative digits: $-237 \to ca3$
The one real advantage to numbers written this way is that the negative sign is only used once per number to say whether a positive or negative, while each of these digits may be used abundantly throughout the number. A disadvantage is that the range of positive numbers expressible in $n$ digits is cut down, since the same number of digits need to express negative numbers. Of course, another disadvantage is for being used to the normal system: it's a mindbender to interpret $4b6cc31$.
This is simple enough, I'm sure it already exists. What is it?
p.s. Not sure what to tag this other than "number-systems", sorry.