Even parity assignment Given the 7-bit code 1100001, append a single parity bit so that the overall 8-bit word has even parity.
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
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A11100001
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B1100001
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C01100001
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D01110101
Answer
Correct Answer: 11100001
Explanation
Introduction / Context:Parity bits are used in simple error detection schemes. With even parity, the total number of 1s in the transmitted word (data bits + parity bit) must be even.
Given Data / Assumptions:
- Data bits: 1100001.
- We will prepend one parity bit to form an 8-bit word.
- Even parity required.
Concept / Approach:Count the number of 1s in the data. If the count is odd, set parity bit = 1 to make the total even; if the count is even, set parity bit = 0.
Step-by-Step Solution:
1) Count ones in 1100001 → 1+1+1 = 3 ones (odd).2) For even parity, parity bit must be 1 so total ones become 4 (even).3) Prepend parity to data: 1 1100001 → 11100001.4) Verify: number of 1s in 11100001 is 4 (even), so parity condition holds.Verification / Alternative check:Try parity bit = 0 → 01100001 gives 3 ones (odd), which violates even parity. Therefore parity bit must be 1.
Why Other Options Are Wrong:
- 1100001: No parity bit added.
- 01100001: Parity bit 0 yields odd total 1s.
- 01110101: Unrelated pattern; parity does not align with the given data bits.
Common Pitfalls:Appending parity at the wrong end, miscounting the number of ones, or confusing even with odd parity.
Final Answer:11100001