Carry chain
Beginner
A special fast wire that passes the ‘carry the one’ from each bit of an adder to the next.
Novice
Dedicated logic and wiring between neighboring logic elements that passes an adder’s carry bit along without going through the general routing, which makes adders and counters much faster and smaller.
Expert
A hard ripple (sometimes with short lookahead) path through each logic block, cascading to the next block in a column. Delay stays linear in width, but each hop is far shorter than a LUT plus routing hop.
Explained in Lookup tables and the FPGA fabric (Architectures).
See also: Logic block (CLB, LAB, slice, ALM), LUT (lookup table).