By using full adder, a single 1-bit binary adders can be constructed from basic logic gates as shown below

But what if we wanted to add together two n-bit numbers, then n number of 1-bit full adders need to be connected or “cascaded” together to produce a adder known as a Ripple Carry Adder.

Ripple carry adder is simply “n“ number of 1-bit full adders cascaded together with full adder representing a single weighted column in a long binary addition. It is called a ripple carry adder because the carry signals produce a “ripple” effect through the binary adder from LSB to MSB.

Let us consider a three bit full adders to “add” together two 3-bit numbers, the two outputs of the first full adder will provide the first place digit sum (S) of the addition plus a carry-out bit that acts as the carry-in digit of the next binary adder. The second binary adder in the chain also produces a summed output (the 2nd bit) plus another carry-out bit and we can keep adding more full adders to the combination to add larger numbers, linking the carry bit output from the first full binary adder to the next full adder, and so forth. An example of a 3-bit adder is given below.