If we suppose that we are given two numbers $a$ and $b$ to add, what circuit depth do we require to add them?
I'm wondering if $a$ and $b$ are $O(n)$, and thus the amount of bits required to store $a$ and $b$ are $O(\log_2(n))$, how much time and/or space we must require to add them.
I'm interested in the general case. However, I am wondering if there is anything else to be said about the case of adding $a+2a+1$. It would be spectacular if we could do this addition in constant circuit depth.