Anticipating carriage
Babbage's fix for addition's slowest moment: doing every carry at once instead of one column at a time.
In addition a carry can ripple through an entire number — 999,999 + 1 forces one across six digits. Handled a column at a time, the worst case takes as many steps as the number has digits, and for Charles Babbage's projected Analytical Engine, working to fifty digits, that was unacceptably slow.
So Babbage built a mechanism that sensed in advance where carries would be needed and performed them in a single motion, making the carry take nearly constant time regardless of length. This anticipating carriage was among the engine's cleverest and most laborious assemblies, and its idea — computing all carries in parallel ahead of time — is precisely what carry-lookahead adders do inside today's processors, a good century on.