Hamming code facts for kids

A Hamming code is a special way to find and fix mistakes in digital information. Imagine you're sending a secret message, and you want to make sure it arrives exactly as you sent it, even if some parts get jumbled up. That's what Hamming codes help with!

The code is named after Richard Hamming, a brilliant scientist who created it in the 1950s. Back then, computers used punched cards to store and read data. These cards often got damaged or had errors, and people had to manually check and fix them. Hamming wanted to find a way for machines to correct their own mistakes, and that's how Hamming codes were born!

How Hamming Codes Work

Hamming codes are used in many places today, like when you're using your phone for telecommunications or when computers process digital signals. They work by adding extra bits of information to your original data. These extra bits are called parity bits.

What are Parity Bits?

A parity bit is like a tiny checker. It tells you if a group of bits (which are just 0s and 1s) has an even or odd number of 1s.

In a Hamming code, each piece of your original data is checked by several parity bits. If an error happens, these parity bits can tell exactly where the mistake is. Not only can they find the error, but they can also often fix it automatically!

Adding Extra Information

Hamming codes use something called redundancy. This means they add more information than strictly needed to send your message. It's like sending a message twice, but in a smarter way, so you can pinpoint errors.

For example, a common Hamming code is called (7,4). This means that for every 4 bits of your actual data, the code adds 3 extra parity bits. So, the total length of the "code word" (your data plus the parity bits) becomes 7 bits. These extra bits are what allow the code to detect and correct errors.

A Simple Example

Let's look at the shortest Hamming code, called (3,1). This code uses 2 parity bits for just 1 bit of your actual data.

Imagine your data bit is either a '0' or a '1'.

• If your data is '0', the code might send '000'.
• If your data is '1', the code might send '111'.

Now, what if there's an error?

• If the code sends '000' but you receive '001', '010', or '100', the Hamming code knows that the original message was '000' and fixes the error.
• If the code sends '111' but you receive '011', '101', or '110', the Hamming code knows the original message was '111' and corrects it.

This way, even if one bit gets flipped by mistake during transmission, the Hamming code can figure out what the original message was and fix it!

See also

• In Spanish: Código Hamming para niños