What is a Multiplexer? How is it different from a decoder? Draw the circuit diagram for an 8:1…

Multiplexer: a combinational circuit that has $2^n$ data input lines, n select (control) lines and a single output. It selects one of the data inputs, according to the select lines, and passes it to the output (many-to-one, a data selector). Difference from a decoder: a decoder has n input lines and $2^n$ output lines, has no data inputs, and activates exactly one output line for each input combination (one-to-many); a multiplexer has $2^n$ data inputs with select lines and only one output line that carries the selected data. 8:1 Multiplexer: 8 data inputs D0 to D7, 3 select lines S2 S1 S0 and one output Y. $Y = S_2'S_1'S_0'D_0 + S_2'S_1'S_0D_1 + S_2'S_1S_0'D_2 + S_2'S_1S_0D_3 + S_2S_1'S_0'D_4 + S_2S_1'S_0D_5 + S_2S_1S_0'D_6 + S_2S_1S_0D_7$ Circuit: eight 4-input AND gates (each data input with one select combination) feed one 8-input OR gate giving Y.