Minimizing the Number of Carries in Addition
Minimizing the Number of Carries in Addition
When numbers are added in base $b$ in the usual way, carries occur. If two random, independent 1-digit numbers are added, then the probability of a carry is $\frac{b-1}{2b}$. Other choices of digits lead to less carries. In particular, if for odd $b$ we use the digits $\{-(b-1)/2, -(b-3)/2, \ldots …