Is it true that the number of carries, when calculating the sum of a finite set of finite positive integers, is constant (i.e. independent of their permutation and the order in which the additions are carried out)? Carries are computed in base 2, so that 1+3 is $01_2+11_2=100_2$, which involves 2 carries: the least significant digits resulted in a carry, which then causes a second carry of the 2's digit.

In case the assumption is wrong, I would also like some ideas for determining the optimal permutation and order of additions.