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:
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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