Parity, Checksums and Error Correction

An even-parity bit makes the total number of one bits in the protected unit even; odd parity makes it odd. The receiver recomputes the property. A single flipped bit changes parity and is detected, while two flipped bits can preserve it and escape detection.

Parity does not identify which data bit is wrong in a simple single-parity-bit scheme. Detection may trigger retransmission if the protocol supports it. The parity convention and which bits are included must be agreed before calculating the extra bit.

A simple majority scheme can send each bit three times and decode the most common received value. Received 110 is interpreted as 1, correcting one erroneous copy in that group. Two wrong copies can cause an incorrect majority, so correction is limited by the assumed pattern of faults.

The extra transmissions increase storage or bandwidth. More sophisticated coding schemes can make different trade-offs, but they should not be confused with the simple method provided in a question. State whether the task requires error detection, recovery by retransmission or direct correction.

A checksum combines values using an agreed algorithm; the receiver compares its own calculation with the transmitted check. A toy sum modulo 256 is easy to calculate but different data can have the same result. A check digit similarly validates a code using a specified weighted or modular rule.

Check digits can reveal some transcription errors without proving the code belongs to the intended person or item. Error checks address accidental corruption under their model. An attacker able to alter both message and an unprotected check may forge a match, so these simple schemes are not authentication mechanisms.

Attempt the task before opening its worked response. Record each change of state, explain the rule used, and check the result against the original requirements. Code examples labelled Python 3 use that language’s conventions; pseudocode states its own assumptions.