Every adder trades depth against area and wiring. Ripple is small and slow, lookahead and select shorten the carry at added cost, and prefix trees reach logarithmic depth with wider wiring.
Family | Depth order | Area order | Wiring |
|---|---|---|---|
Ripple-carry | N carry stages | N full adders | Local neighbour wires only. |
Carry-lookahead | Group levels, not N | Groups plus lookahead gates | Wider fan-in inside each group. |
Carry-select | Block delay plus muxes | Approaches twice the ripple for many blocks, plus muxes | Select wires across blocks. |
Prefix | Ceiling of log2 N levels (Brent-Kung about twice) | Brent-Kung, then Sklansky, then Kogge-Stone | Dense tracks or high fanout. |
Lesson | What it covers |
|---|---|
Full-adder chain, linear delay, and area of N adders. | |
Generate and propagate signals with grouped carries. | |
Precomputed blocks chosen by a carry mux. | |
Kogge-Stone, Brent-Kung, and Sklansky trees with a runnable model. | |
How synthesis maps plus, and carry-save for many operands. |
Ripple delay grows linearly with width while prefix depth grows logarithmically. Past a few bits the depth win exceeds the area cost.