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I found the data sheet for this multiplexer/demultiplexer, and as I understand it, when channel 5, for example, is active (I5), S0 and S2 would be active, making the S nibble 0101.

The question is, if there were multiple channels active, say 5 and 6, what would S be?

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S0..S3 are for selecting the active channel. They are digital inputs, not outputs.

Only one channel at a time (at most) is connected to the "common input/output". All the others are floating. If /E is '1' then the common input/output is floating (no channels are connected).

It acts just like a selector switch- with an 'off' position. When the selection inputs are 0x0101 and /E is '0' then channel 5 is active, which means that I5 (pin 5) is connected to common input/output (pin 1) through something like 100 ohms typically. The other I0..I4 and I6..I15 are floating.

The multiplexer acts like a resistor when it's 'on', so it doesn't really care if you use the I pins as outputs or as inputs. It also doesn't care if the signals on I0..I15 or common input/output are logic levels or are some other voltage between the power supply rails- 100mV or whatever. Hence the name Analog Multiplexer/Demultiplexer

If you want to connect multiple things at once, you can use individual switches, or if you have a many-to-many matrix, a crosspoint switch.

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