Ripple Carry Adder (RCA)
Simplest adder: carry ripples bit-by-bit from LSB to MSB.
Problem
Add two n-bit binary numbers with minimum hardware.
How it works
Chain n full adders in series. Bit 0’s carry-out feeds bit 1’s carry-in, and so on. Each FA must wait for the previous carry: the carry ripples from LSB to MSB sequentially.
Key insightDelay grows linearly with width: doubling n doubles the delay.
Tradeoffs
- Area
- n FA (minimum possible)
- Delay
- 2n gate delays
- Best when: n is small or area is the primary constraint.