Hello,

1. Data selection
2. Multiplexed displays
3. Logic function generation
4. Simple communications systems

Multiplexers are devices that take multiple inputs and route them to a  single output.  The output is determined by the data select input.  The  binary input selects which device signal is put through to the output.

Multiplexed displays like the 7-segment display use a mux to send the  data to all displays on a timed sequence of a data select signal.  The  data select signal will also be used by a decoder to select which  display to activate.  The activation of the individual displays  sequences with the data from the multiplexer at a rate that, to the  human eye, looks like all displays are activated simultaneously with the  correct display on each. 

Logic function generation with a multiplexer is done by setting the  data inputs to the desired logic table output then the data select input  is used to select the desired logic/input to send to the output.  So,  if you wanted an output of 1 for binary inputs 001, 011, and 101, you  would connect VCC to the input contacts for decibels 1, 3, and 5 to be  routed to the output when that data input is selected.

Communication with multiplexers can be simple for a small system like  a security system switching from one camera to the next every few  seconds or recording all at the same time but in different files.  It  could use a multiplexer to select which camera is recorded and the  demultiplexer to select the correct file for that specific camera.  It  can switch from one to the next at such a rate that it seems that it is  all being done at once.  I know from my experience working on F-16s that  every system on that jet communicates through multiplex buses.  Each  system will communicate back to a central processor that uses  multiplexers and demultiplexers to talk to several systems at the same  time switching from one to the other.  Radio communication is similar,  jumping from one frequency to another.  The frequencies are being  changed so fast that a radio on a single frequency only hears Decepticon  sounds, but the guy on the other radio switching the same frequencies  at the same time hears everything.

Floyd, T. L. (2014). Digital Fundamentals (11th ed.). Pearson Education (US).

https://ecpi.vitalsource.com/books/9780133524390