How an address appears
Positions 1–7 carry three-bit binary names. Each parity beam watches the positions containing its bit. XOR the names of the lit positions and failed beams spell the changed position.
Damage that carries its own address
The Error
Points Home
Four data bits become eight lamps. Touch one to damage the message: the failed parity beams intersect at the exact lamp that changed.
corrects any 1-bit error
detects any 2-bit error
locks repair at 3+ visible flips
detects any 2-bit error
locks repair at 3+ visible flips
Sixteen valid payloads · choose one
payload A · 1010
sent strip 10110100
sent strip 10110100
parity beams quietmessage intact
syndrome 000 · overall parity even
No failed checks; there is no error address.
No failed checks; there is no error address.
The eighth lamp
p∞ watches the whole strip. If it rings with a nonzero syndrome, one bit changed. If it stays quiet while the syndrome is nonzero, an even number changed: detect, but do not guess.