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The multiplexer, or MUX, will cycle through a certain number of input, based on its input capabilities and the desired selection. The MUX has any number of inputs, with each being connected to a certain analog input (Johnson, 2006).  The MUX basically acts like a set of switches that open and close based on address commands from the control PC.
The analog-to-digital converter and sample-and-hold circuitry perform analog-to-digital conversions, usually by successive approximation, although other methods are available, and a fast S/H circuit (Johnson, 2006). Because these devices are contained in the same component, then the distance between them can be minimized, and can even be incorporated into each other as much as possible, and so the ADC conversion rate can be kept to a minimum.
There is an address decoder and command processor that interprets the commands sent from the PC, and the addresses they are intended for (Johnson, 2006). The address lines can select the MUX, S/H circuit, ADC, or DAC latch, and then send commands to each of those based on their capabilities, such as which line to read from, sample or hold, start/stop conversion, or latch/unlatch the DAC latch.
The DAC can convert the data on the digital data bus into an analog output. The latch is there to ensure that the correct data is transformed to an analog output, but also so that the data bus can output more data for other processes.
An example of an industrial data acquisition system is a physical vapor deposition tool that my company is currently developing, and controllers developed to control that tool. For one specific example, a degas oven uses many RTDs to control its temperature, and the DAS is used to multiplex and convert those analog signals into a digital input, and then a digital output is used to control heaters and fans so that the temperature is held uniform throughout the system.
Works Cited
Johnson, C. D. (2006). Process Control Instrumentation Technology. Upper Saddle River, NJ: Pearson Prentice Hall.

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