Logic function generation
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).