What is Hamming code 

Hamming code is an error-correcting code used to detect and correct single-bit errors in binary data. Developed by Richard Hamming, it adds redundant bits to the original data bits to create a code word that can be used to identify and correct errors. Here’s a brief overview:

1. **Redundant Bits**:

   - **Parity Bits**: Hamming code adds extra bits (parity bits) to the original data bits. These bits are calculated based on specific patterns of the data bits to create a code word that includes both the original data and parity information.

2. **Encoding**:

   - **Positioning**: Parity bits are placed in specific positions within the code word, typically at positions that are powers of 2 (1, 2, 4, 8, etc.).

   - **Calculation**: Each parity bit checks the parity (even or odd) of certain bits in the code word. The pattern of parity checks helps in detecting and locating errors.

3. **Error Detection and Correction**:

   - **Syndrome Calculation**: When data is received, the Hamming code checks the parity of the received bits. If an error has occurred, the pattern of incorrect parity checks helps determine the exact position of the error.

   - **Error Correction**: By identifying the position of the erroneous bit, the Hamming code can correct the single-bit error and recover the original data.

4. **Example**:

   - For a 7-bit Hamming code, 4 bits are data bits and 3 bits are parity bits. The parity bits are calculated based on combinations of the data bits, allowing detection and correction of single-bit errors.

5. **Applications**:

   - **Memory Systems**: Hamming codes are commonly used in computer memory systems (e.g., ECC RAM) to detect and correct errors in stored data.

   - **Communication Systems**: They are also used in digital communication systems to ensure data integrity.

In summary, Hamming code is a technique for error detection and correction that adds redundancy to data in the form of parity bits, allowing for the detection and correction of single-bit errors in the transmitted or stored data.