What a majority gate computes

A 3-input majority gate (MAJ3) outputs 1 whenever at least two of its three inputs are 1 — Boolean expression A·B + B·C + A·C. A 5-input majority gate (MAJ5) generalizes the idea: output 1 whenever at least three of the five inputs agree. Boolflow ships both as ready-made blocks.

From voting to fault tolerance

Triple modular redundancy runs the same logic three times, in three physically separate copies, and feeds all three outputs into a MAJ3 gate instead of using any one copy's output directly. If one copy is damaged or misbehaves, the other two still agree with each other and outvote it — the system's output stays correct even though one third of its hardware failed.

Detection versus correction

This is a fundamentally different guarantee than the parity bit from Gray code and parity: parity only detects that something went wrong, with no way to tell which bit or how to fix it. Majority voting corrects the fault automatically, in the same clock cycle, at the cost of running the entire logic three times over instead of adding one extra bit — which is why it shows up in aerospace and medical electronics rather than everyday circuits.

Try it yourself

Build three separate copies of a small circuit — say a comparator — feed all three outputs into a MAJ3 block, then force one copy's output wrong by hand and confirm the MAJ3 output still matches the other two. See the Help reference for MAJ3 and MAJ5's exact pin layout.