How does the Hamming code work?

Question

When transmitting data, the Hamming code apparently allows you to recreate data that has been corrupted over the wire (an error correcting code).

How does this work

Answer 1

@GameCat and what about 2-bit error detecting code.

In this case lets say 111 has changed to 100. Then we can be sure that there are 2 bits wrong and we know this because the distance between 111 and 100 is 2 bits, and the distance of 000 and 100 is 1 bit. So if we know that there is 2-bit error we can be sure what is the right value.