multiplexer
As far as I know, analogue multiplexing is used to take voltage samples from many channels in a short time. It passes the voltages from an input to the ADC without amplifying them. I guess buffer them?
But is that called analogue because of the inner circuitry or because of its operation? And what is a digital multiplexer used for?
If you are going to continue to use 256 amplifiers, ADCs, etc. you will need a sample and hold that is triggered each time you activate the mux channel. One thing you'll have to pay attention to is the droop rate of the SH.
Alternatively you could now get away with a single amplifier, ADC, etc. for each group of 4 or 16 channels. You would know which channel was being sampled because you are driving the mux to select the proper channel. This would greatly reduce the system complexity if you are able to do it.
Note for any of these configurations you will now have to send several signals to your mux to select the proper channel. This means you'll need some device to handle the sequencing, and this device could also be used to handle the triggering of the SH amplifier, or the per block ADC.
If you were running the LEDs in series then yes, you would need a higher voltage. You aren't though - otherwise they'd all be on or all be off. You are running them in parallel.
From what I understand of your description you have the one output of the '595 going into the anode of the all the LEDs of one column. The cathodes of these LEDs then go into separate inputs of the TLC for PWM.
And, as you say, the '595 can supply 35mA of current per output. That is enough for to light one LED reliably.
You will need to supply 6 times that current for 6 LEDs.
The simplest way would be to use a single transistor and resistor per column. For example, the '595 output connects to the base of an PNP transistor through a 1KΩ (for example) resistor. The emitter connects to Vcc, and the collector connects to the LEDs in the same way the output of the '595 used to. When the '595 sets an output low it turns on the transistor which then allows the current to flow from Vcc to the LEDs.
You can't use the TLC with, for example. a ULN2803 as they are both current sinks. You need something which can be a current source, which a transistor can be.
Best Answer
The operation of any multiplexer (MUX for short) is conceptually the same, be it analog or digital.
In essence you have a set of numbered data inputs (usually a power of 2, say \$N=2^n\$ inputs named, say, \$X_0, X_1,\$ ... etc.), a set of digital selection inputs (in number of \$n\$) and an output. A mux works by sending one (and only one) data input signal to the output. The data input to be "routed" to the output is the one selected using the selection inputs, i.e. the one whose number, expressed in binary, is put on the selection inputs.
In other words, a mux acts like a digitally-selectable single-pole/N-throw switch.
The difference between analog and digital muxes, seen from the outer world, is that the data inputs and the output are digital (two-level) for digital muxes, whereas in analog muxes the data signals can be analog.
The common implementation, in the two cases, is quite different. Analog muxes are made using FET switches (most commonly MOSFET transmission gates) and they act more like actual switch arrays, without amplification of the switched signals.
Take as an example the common 74HC4051 analog mux:
Here S0, S1 and S2 are the selection inputs, /E is the enable input (all four pins are digital), whereas Y0..Y7 are the analog data inputs and Z is the analog output. Note that in this case you can also reverse the role of the analog inputs and output and get a demultiplexer (a.k.a. DEMUX).
In particular, see how a single switch is implemented:
Digital muxes, on the other hand, use a bunch of digital logic gates to steer signals from (digital) inputs to the (digital) output. Digital muxes amplify the signal, since the internal gates are, after all, buffer amplifier.
You can refer to the Wikipedia article about the mulitplexer to understand how a digital multiplexer works internally. Actual implementations don't differ too much.
Take as an example the common 74HC151 digital mux and its internal logic diagram:
In this case they use I0,I1,...,I7 for the data inputs and Y for the output (they also provide a negated output for free).