Odd parity bit for 1011001 — parity and checksum
introthe opposite convention
Answer
1
Why this example is worth doing
The same data under the odd convention gives the complementary bit. Neither convention is better, but the two ends of a link must agree, and a mismatch produces a system that reports an error on every single word — a failure mode distinctive enough to diagnose from the symptom alone. The page mentions that odd parity has one practical edge: an all-zeros word is invalid, so a dead line is detected.
Try your own input in the Parity & checksum. Even and odd parity, one’s-complement sums and the Internet checksum, step by step.
How the answer is reached
Odd parity of 7 bits
Data1011001
Ones in the data4— even weight
Odd parity: choose the bit that makes the total number of 1s odd, so the parity bit is the complement of the XOR of all data bits.
p (odd)1— total ones becomes 5
Codeword (parity appended)10110011
Codeword (parity prepended)11011001
A single parity bit detects every odd number of bit errors and is blind to every even number. It can never correct anything: d_min = 2.
Source: R. W. Hamming, Bell System Technical Journal 29(2):147–160 (1950)