Even parity bit for 1011001 — parity and checksum
intromake the total number of 1s even
Answer
0
Why this example is worth doing
The data has four 1s, already an even count, so the even-parity bit is 0. The page states the rule as the invariant it is — the transmitted word including the parity bit must have an even number of 1s — rather than as a recipe, because the invariant is what the receiver checks and the recipe is only how the sender achieves it.
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
Even parity of 7 bits
Data1011001
Ones in the data4— even weight
Even parity: choose the bit that makes the total number of 1s even, so the parity bit equals the XOR of all data bits.
p (even)0— total ones becomes 4
Codeword (parity appended)10110010
Codeword (parity prepended)01011001
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)