In error control, what is a parity bit and how is it used when appending control information to a string of binary digits?

Difficulty: Easy

Correct Answer: a check bit appended to a binary string to make the total number of 1s conform to a chosen parity (even or odd)

Explanation:


Introduction:
Parity is one of the simplest and oldest error-detection schemes. By adding a single bit that reflects the parity (evenness or oddness) of the number of 1s in a data word, systems can detect many single-bit errors with minimal overhead. While modern networks prefer stronger codes (CRC), parity remains pedagogically important and still appears in memory systems and serial protocols.


Given Data / Assumptions:

  • A binary string (e.g., a byte) is to be transmitted or stored.
  • We choose either even parity or odd parity convention.
  • We seek a definition of the parity bit itself.


Concept / Approach:
A parity bit is appended to the data so that the total count of 1s, including the parity bit, satisfies the chosen rule. For even parity, the parity bit is set such that the total number of 1s is even; for odd parity, it is set so that the total is odd. At the receiver, the parity of the received bits is recomputed and compared—if it does not match the expected parity, an error is detected. Parity detects all single-bit errors and some multi-bit patterns, but it cannot correct errors nor detect all multi-bit errors.


Step-by-Step Solution:
1) Choose a parity convention (even or odd).2) Count the number of 1s in the data word.3) Set the parity bit so that total 1s (data + parity) matches the convention.4) On reception, recompute parity and compare; mismatch indicates an error.


Verification / Alternative check:
Practical interfaces like RS-232 allow an optional parity bit in the frame (start, data bits, optional parity, stop), illustrating live usage of this concept.


Why Other Options Are Wrong:

  • Checksum (option A): uses multi-byte arithmetic sums, not just a single parity bit.
  • Syntactic codes (option C): relate to language/grammar constraints, not parity.
  • Error rate (option D): a performance metric, not a code definition.
  • None of the above: invalid because option B is correct.


Common Pitfalls:
Assuming parity can correct errors; it only detects certain error patterns and is weaker than CRCs or Hamming codes.


Final Answer:
a check bit appended to a binary string to make the total number of 1s conform to a chosen parity (even or odd)

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