Truth Tables

A truth table lists a gate's output for every combination of inputs. For a 2-input gate there are $2^2 = 4$ input rows; for $n$ inputs there are $2^n$ rows. Here is AND:

| a | b | a AND b | | --- | --- | --- | | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 |

Truth tables completely specify a classical gate. Quantum gates need a richer description — a matrix of complex amplitudes — precisely because they can act on superpositions of all those input rows at once.

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How many rows does a truth table for a gate with 3 inputs have?

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