Parity, SEC & DED, Hamming Code

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Parity

• Parity is a simple error detection technique. It helps identify whether a single-bit error has occurred during data transmission or processing.
• Parity can only detect single-bit errors—it cannot correct them.
• It fails to detect if two are more bits are changed since the parity may remain the same

Even vs Odd

• Even → number of 1s in a byte (including parity bit) is even
• Odd → number of 1s is odd

Detection and Correction

• Detection → did bits flip?
• Correction → flip the bits back

SEC & DED

• Improves parity by detecting 2 bit errors and correct 1 bit errors
• SEC → single error correction
• DED → double error detection

Hamming Code

• Place multiple parity bits at certain positions in the number
  • Positions are powers of 2
• Formatted as , where is the total bits and is the number of data bits

Example

• → transfer 4 data bits,

Set Positions

• The data bits can be placed at the positions that are not powers of two
• The data would be

Parity Bits

• XOR is used to ensure each group has even parity
• checks 1, 3, 5, 7 →
• checks 2, 3, 6, 7 →
• checks 4, 5, 6, 7 →
• Final value →

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