No error, one error, and two errors show what the correction table can and cannot accept. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
No-error lookup keeps the word accepted
Word 111 has syndrome 00, correction index -1, and accepted bit 1.
s=00c=−1a=1
One middle error repairs back to the code word
Error word 101 repairs to 111 with accepted bit 1.
wfixed=111a=1
Two errors can look like one but fail acceptance
Double-error word 001 repairs to 000 instead of the original word, so accepted bit 0 is checked low.