Fan-in
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Fan-in is the number of inputs of an electronic logic gate. For instance the 'fan-in' for the AND gate shown below is 3. Logic gates with a large fan-in tend to be slower than those with a small fan-in, because the complexity of the input circuitry increases the input capacitance of the device.
A related concept is fanout, which is the number of logic inputs that a given logic output drives.
Maximum limits on fan-out are usually stated for a given logic family or device in the manufacturers datasheets. More complex analysis than fan-in and fan-out is required when two different logic families are interconnected.