Negate an integer in a negative base What is a simple algorithm you can feasibly do by hand to negate an integer in a negative base, such as negadecimal? In positive bases, you can simply append a negative sign if it is not there, and remove it if it is: Negate 123456 -> -123456 Negate -123456 -> 123456 In a negative base, however, it is not so easy, since both negative and positive numbers can be represented without any sort of explicit sign. This should be the result in negadecimal: Negate 123456 -> 98764 Negate 98764 -> 123456 I can't figure out a straightforward method (i.e. one that can be done with pencil and paper fairly mindlessly) to negate a negadecimal number. How could I do this?

Working from the right, the two extreme digits must add up to 0 or 10 (and can only add to 0 if they are both 0). If they add to 10 then carry one from the next sum. The next two digits to the left must add up to 0 or 10 if not carrying one, or if carrying one then add up to 1 or 11; if they add up to 10 or 11 then carry one from the next sum. And so on.

So starting with say 120034:

* The negative must have 6 on the right as $4+6=10$, so carry one.
* The next digit of the negative must be 8 as $3+8=11$, so carry one.
* The next digit of the negative must be 1 as $0+1=1$, so do not carry one.
* The next digit of the negative must be 0 as $0+0=0$, so do not carry one.
* The next digit of the negative must be 8 as $2+8=10$, so carry one.
* The next digit of the negative must be 0 as $1+0=1$, so do not carry one.
* The next digit of the negative must be 0 as $0+0=0$, and so on.



But we can ignore left-hand leading 0s so the negative of 120034 is 80186.