Hamming Code Generator
Hamming Code Generator calculates the Hamming code for a given binary data string. Enter a binary string (e.g., 1011), and the calculator will determine the number of parity bits (\( r \)), their positions, and generate the complete codeword with parity bits inserted.
Methodology Used in Hamming Code Generator
The Hamming code is an error-correcting code that adds parity bits to a data string to detect and correct single-bit errors. Parity bits are placed at positions that are powers of 2, and each parity bit covers specific data bits based on its position.
Hamming Code Equations:
Number of parity bits \( r \) for \( m \) data bits satisfies:
\[ 2^r \geq m + r + 1 \]Parity bit at position \( 2^i \) checks bits where the binary representation of the position includes \( 2^i \).
Algorithm Steps:
- Input a binary data string of length \( m \).
- Calculate the number of parity bits \( r \) using \( 2^r \geq m + r + 1 \).
- Place data bits in positions that are not powers of 2 in a codeword of length \( m + r \).
- Calculate each parity bit using XOR over the bits it checks.
- Output the final codeword and visualize bit positions.
Hamming Code Generator calculates the Hamming code for a given binary data string. Enter a binary string (e.g., 1011), and the calculator will determine the number of parity bits (\( r \)), their positions, and generate the complete codeword with parity bits inserted.
Methodology Used in Hamming Code Generator
The Hamming code is an error-correcting code that adds parity bits to a data string to detect and correct single-bit errors. Parity bits are placed at positions that are powers of 2, and each parity bit covers specific data bits based on its position.
Hamming Code Equations:
Number of parity bits \( r \) for \( m \) data bits satisfies:
\[ 2^r \geq m + r + 1 \]Parity bit at position \( 2^i \) checks bits where the binary representation of the position includes \( 2^i \).
Algorithm Steps:
- Input a binary data string of length \( m \).
- Calculate the number of parity bits \( r \) using \( 2^r \geq m + r + 1 \).
- Place data bits in positions that are not powers of 2 in a codeword of length \( m + r \).
- Calculate each parity bit using XOR over the bits it checks.
- Output the final codeword and visualize bit positions.