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A Multiplexer or simply a MUX is a type of logic element which enables multiple signals to use a shared line ( the output) The select input S determines which of I0 or I1 gets to be connected to the output signal O The logic is simple: O = ~S.I0 + S.I1 ~ is a not gate . is and gate + is or gate This is a two input MUX which can be used to further build muxes with higher number of inputs. Muxes are very common circuit elements and many times, are more useful for deriving output for complex logic equations of the inputs. They are particularly useful for Busses (collection of signals for communication between circuit blocks) which have multiple Masters ( blocks which can initiate traffic on the bus) where the select signals can be used to grant a particular Master access to the bus. Thus, a mux can be effectively used to connect various circuit sub-blocks using the shared signals based on the value of the select signals, which are usually controlled by the state of the design. Also this circuit element is extensively used for configuration. For example, clock MUX, often have two different frequency clock at their inputs and based on the circuit configuration, a MUX can be used to either allow a higher or lower frequency clock.