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Multiplexer.
A mux (multiplexer) is a is a 1-of-n switch. It can select one of multiple (usually 2,4, or 8) inputs, and connect that input pin to its output pin. Analog muxes such as the CD4051 family can pass an analog voltage; digital muxes such as the 74LS151 pass digital signals.

They are often used to allow a single resource (such as an analog-digital converter) to make measurements on multiple channels (such as multiple faders on a lighting controller).