Multiplexers (MUX) and Demultiplexers (DEMUX) are electrical circuits that are used it many integrated circuits and so. They use an address control line (usually analog) and control the flow of a data signal. The MUX takes many inputs and has one output. The address line controls which of the many inputs goes to the one output. The DEMux has one input and many outputs. The address line controls which of the many outputs is connected to the one input. In either case, only one of the many inputs/outputs is connected to the one output/input.
Multiplexers have many inputs (this number differs for each), but just one output (this number is still the same).
They allow you to control what input is "showing" on the output. Several control signals or switches are used to create the address. The number of address lines depends on the number of inputs (2in=1cs, 4in=2cs etc). Each input has its own binary address which must be "entered" with the control signals. An analog signal may be used for the address signal.
Note that analog data signals will pass properly through the basic logic gates.
Let's try an example:
You have several thermometers placed around your property and want to check them now and again. You can use a mux (multiplexer) to be able to read them each from just one place. Just set the switches to choose the one you want to read. You can only see one at a time but you won't have to run around to look at them.
Now a pic of Multiplexer, also with labels -
Demultiplexer (as you can guess, according to its name) does exactly the opposite thing. DEMUX has only one input (still just one), but many outputs (this number differs for each application).
It allows you to control which output will "follow" the state of the input. Again, several control lines or switches are used to address the specified output. The number of address lines depends on the number of outputs (2out=1cs, 4out=2cs etc) or it could be an analog signal. Each output has its own address in binary code which must be "entered" on the control signals.
Here's an example of use:
You have a stable with 8 stalls and have gates on each one. You want to be able to open and close only one gate at a time. Use a demux to let you set the door number and then just one door button.
Here is a picture of Demultiplexer with labels -
A demux circuit may not even include a data input depending on the application. The proper output line may be set active as soon as the address is established. An example is an electric 'sundial' clock face which will always have one and only one point lit around the circle.
A much simplified demux may be made with memory banks. One or both of the address inputs are connected to the address line in the demux. Memory banks always have to be programmed properly for their use. The simple demux only needs an 'F' in proper address, which depends on the application.
If you need to pass an analog signal, that can go to the other address input but the memory has to be programmed properly. Remember that analog signals do not 'pass through' a memory. Or the demux output can go to an AND gate with the analog signal going to the other input.
Now you should understand how do MUX and DEMUX work. If you want to look at them in detail or just rebuild them into your world, this world link should help you.
NOTE: I tried to write this guide in "normal language" (that means I did not use too technical names and so). If you still can't understand, or if you've found any mistakes, PM me on the wiki or on forums - name is JustPlaying. I will try to correct all my mistakes and make this guide better and easier to understand.