What is a multiplexer and how does it work?

A multiplexer (MUX) is a combinational circuit that selects one of multiple input signals and forwards it to a single output based on select lines. A 2:1 MUX has 2 inputs, 1 select line, and 1 output; a 4:1 MUX has 4 inputs and 2 select lines. For n select lines, there are 2^n possible inputs. Multiplexers are used in data routing, time-division multiplexing, and can implement any Boolean function by connecting inputs to 0 or 1 appropriately.