A multiplexer (MUX) is a combinational digital data selector that directs one of 2^N input lines to a single common output line using N binary selection lines. In a 4-to-1 multiplexer, two select control bits (S1, S0) decode to enable one of four internal AND gates, channeling the selected input signal through a unifying OR stage. Multiplexers form vital routing switches for ALU operand selection, data bus steering, and FPGA logic implementation.