TITLE: Negate an integer in a negative base
QUESTION [5 upvotes]: 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?

REPLY [3 votes]: 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.