Majority voter
A majority voter is a combinational circuit whose output is 1 when more than half of its inputs are 1, so with three inputs it is 1 when at least two of them are.
High when at least two of three inputs are.
Circuit diagram
Toggle the inputs and follow the signals: green wires are high, red are low. The highlighted row of the truth table below is the one you have set.
Truth table
| A | B | C | out |
|---|---|---|---|
| 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 | 1 |
| 1 | 1 | 1 | 1 |
Boolean expressions
- out
- a ∧ b ∨ b ∧ c ∨ a ∧ c one AND per pair, then OR
How it works
Three inputs vote and the majority wins. It is the same function as the carry out of a full adder, which is worth noticing: adding three bits produces a carry exactly when at least two of them are 1.
Where it is used
- Redundant systems, where three copies of a circuit vote so one failure is outvoted.
- The carry path of an adder.
- Smoothing a noisy signal by voting over three samples.
Build it
Three ANDs and one OR. It cannot be made smaller as a sum of products, which the Karnaugh map solver will confirm.
Or draw it from the expressions above with the circuit diagram generator, in either symbol standard, and export it as SVG, PNG, Verilog or VHDL.
Reference card
The diagram above as an image, black on white, for notes or a slide.
Click to download: Majority voter circuit diagramQuestions about the majority voter
What is a majority voter used for?
Fault tolerance. Run three copies of a circuit and vote on their outputs, and a single failing copy is outvoted, which is triple modular redundancy as used in aircraft and spacecraft. The same function is the carry out of a full adder, and it also cleans up a noisy signal by voting over three samples.
What is the boolean expression for a 3-input majority function?
(A ∧ B) ∨ (B ∧ C) ∨ (A ∧ C): one AND per pair of inputs, then an OR. Any pair being 1 is enough. This is the smallest sum of products form there is, which a Karnaugh map confirms, and it is exactly the carry out equation of a full adder.