Parity cannot detect two errors — parity and checksum
corethe fundamental limitation
Answer
0
Why this example is worth doing
Flip two bits and the count's parity is restored, so the check passes and the corruption goes undetected. This is the honest limitation of a single parity bit: it catches any odd number of errors and no even number. The page shows a concrete pair of flips rather than stating the rule abstractly, and uses the gap to motivate every stronger scheme on the page and on the Hamming page.
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
Data1111101
Ones in the data6— 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 6
Codeword (parity appended)11111010
Codeword (parity prepended)01111101
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)