Is it a PC or a PLC? OK, that doesn't matter. I assume that you are talking about analogue inputs and that usually means having one analogue-to-digital converter. Good A/D converters are (or used to be) quite expensive, so using one for each channel is (was) considered a luxury that few can (could) afford.
So, a set of switches are used to connect one analogue input at a time to the A/D. A value is read from the A/D and the next channel switched to the A/D. It is this switching that got the name multiplexing.
The switches can be little relays (you will hear the switching, sounds like little animals moving inside a tin box) or they can be solid state (transistor, FET and CMOS) switches. They are quiet. Nothing can be heard.
Multiplexers typically switch 8 or 16 channels. Multiplexing can be quite fast if you have solid state switches and usually not faster than 10 or 20 channels/seconf if you have relay switches.
The cross-talk between channels is generally better with relays, but modern solid state switches are also very good.
Gunnar Englund
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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...