The Radio Signal Filter
Clean the signal for transmission. The OUTPUT must be true only if SIGNAL and NOISE are different, but also requires FREQ to be active.
Replay this puzzle All puzzles
The truth table
Inputs on the left, the output on the right. A circuit solves the puzzle when it reproduces every row.
| SIGNAL | NOISE | FREQ | OUTPUT |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 |
What the table tells you
- OUTPUT is 1 in 2 of the 8 rows. Every input matters: for each one there is a row where flipping it changes OUTPUT. The rows that turn it on: SIGNAL=0, NOISE=1, FREQ=1; SIGNAL=1, NOISE=0, FREQ=1.
The smallest known circuit: 2 gates
As a formula, one line per output:
OUTPUT = ((SIGNAL XOR NOISE) AND FREQ)
As a netlist, in the order you would wire it. Each g is one gate; the last line says which signal drives the output.
g1 = SIGNAL XOR NOISEg2 = FREQ AND g1OUTPUT = g2
The search ran out of budget before it could rule out every smaller circuit, so 2 is the best anyone found, not a proof. If you build it in fewer, the leaderboard records it. Gates that do not feed an output are never counted.
Leaderboard for the day
Nobody posted a result on the day. The circuit above is the reference.