Even parity assignment Given the 7-bit code 1100001, append a single parity bit so that the overall 8-bit word has even parity.

Difficulty: Easy

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

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