Ripplecarry

Ripple-carry adder is a digital circuit that computes the sum of two binary numbers by connecting a chain of full adders. Each full adder receives a pair of input bits and a carry-in, and produces a sum bit and a carry-out. The carry-out of one stage is wired as the carry-in to the next stage, creating a ripple of carries from the least significant bit to the most significant bit.

An n-bit ripple-carry adder requires n full adders. The sum bits can be produced in parallel after the final stage, but the carry signal must propagate through all stages sequentially. Consequently the overall delay is proportional to n, making large-word additions slower than alternative adder architectures.

Advantages include simplicity, small area, and ease of implementation across technologies; it is suitable for small word sizes and as an educational example of propagation. Drawbacks include high worst-case delay due to long carry chains, potential latency variability with input patterns, and less favorable power characteristics for long chains.

Alternatives such as carry-lookahead, carry-select, and prefix adders reduce carry propagation delay at the cost of increased circuit complexity and area. In practice, ripple-carry adders appear as core components in simple ALUs, educational materials, or within larger arithmetic units where maximum speed is not critical.

Implementation notes: in hardware description languages, an n-bit ripple-carry adder is often described as an array of n full adders. Each full adder can be built from basic gates or realized using standard cells or lookup tables in ASIC or FPGA designs. The concept also generalizes to subtraction and modular arithmetic when combined with complemented inputs and borrow logic.