An odd-parity generator appends a parity bit so that the total number of 1s in the transmitted word is odd. At the receiver, an XOR parity check rejects words whose overall parity is even. Fill in the blanks.

Difficulty: Easy

Correct Answer: odd, even

Explanation:


Introduction / Context:
Parity bits are a classic single-bit error detection method used in memory systems, serial links, and legacy storage. With odd parity, the transmitter ensures the total count of 1s (data bits + parity bit) is odd. The receiver recomputes parity to detect single-bit errors quickly.


Given Data / Assumptions:

  • Parity scheme: odd parity.
  • Receiver uses XOR aggregation for parity checking.
  • Rejection occurs when the check fails the expected parity.


Concept / Approach:
XOR of a set of bits equals 1 if and only if the set contains an odd number of 1s. Under an odd-parity scheme, a correct (error-free) received word should have XOR = 1. If noise flips a single bit, the parity flips and XOR = 0 (even number of 1s), which signals an error and the word is rejected (or flagged).


Step-by-Step Solution:
State the transmitted parity target: odd total count of 1s.Apply XOR property: XOR(all bits) = 1 for odd parity, 0 for even parity.Define the rejection criterion: reject even-parity words under an odd-parity scheme.Fill blanks: “odd, even.”


Verification / Alternative check:
Example: data 1011 has three 1s (odd). Odd-parity bit = 0 to keep total odd (still three). XOR over 10110 = 1, so accept. If one bit flips, say 10100 (two 1s), XOR = 0 (even) → reject.


Why Other Options Are Wrong:
“even, odd” mismatches odd-parity definition. “high/low” and “low/high” are not parity categories. “None” is false because “odd, even” is correct.


Common Pitfalls:
Confusing the parity of data alone versus data+parity; forgetting that XOR implements parity naturally—do not use AND/OR for parity checks.


Final Answer:
odd, even

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