Odd parity generation: An 8-bit binary word is applied to an odd-parity generator. The parity bit will be 1 only if ________.
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Athe number is odd
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Bthe number of 1s in the word is odd
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Cthe number is even
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Dthe number of 1s in the word is even
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Ethe MSB is 1
Answer
Correct Answer: the number of 1s in the word is even
Explanation
Introduction / Context:Parity bits provide a simple error-detection mechanism. With odd parity, the total count of 1s across data bits plus the parity bit must be odd. Understanding when the parity bit becomes 1 is essential for designing and checking parity logic.
Given Data / Assumptions:
- 8 data bits (any pattern of 1s and 0s).
- Odd-parity convention: total ones (data + parity) is odd.
- Single parity bit added to the word.
Concept / Approach:Let k be the number of 1s in the 8-bit word. Odd parity sets parity_bit so that k + parity_bit is odd. Therefore parity_bit = 1 when k is even, and parity_bit = 0 when k is odd. The numeric value of the word is irrelevant; only the count of 1s matters.
Step-by-Step Solution:
Let k = count_ones(data).If k is even → choose parity_bit = 1 to make k + 1 odd.If k is odd → choose parity_bit = 0; odd + 0 remains odd.Thus the parity bit equals 1 only when the number of 1s is even.Verification / Alternative check:Example: data = 10110000 has k = 3 (odd) → parity_bit = 0; total ones = 3 (odd). Another: data = 11000000 has k = 2 (even) → parity_bit = 1; total ones = 3 (odd).
Why Other Options Are Wrong:
- “number is odd/even”: The arithmetic value of the byte does not determine parity; the Hamming weight does.
- “number of 1s is odd”: For odd k, parity bit is 0, not 1.
- “MSB is 1”: Parity depends on all bits, not only the MSB.
Common Pitfalls:Confusing odd vs even parity definitions; focusing on numeric value rather than bit count; omitting the parity bit in the final odd-count requirement.
Final Answer:the number of 1s in the word is even