I have a device that outputs a digital out (5V or 0V signal). I have connected the signal ground to the labjack's FIO0 ground, and the signal to FIO0. With the digital output both on and off, I only read '1' from the FIO0 input. Is this wired correctly?
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If the voltage from FIO0 versus GND is < 0.8 volts it will read low.
https://labjack.com/support/datasheets/u6/appendix-a
Connect a DMM to FIO0/GND at the same time as your signal. I suspect you will see that your signal is not pulling FIO0 below 0.8 volts.
Can you post a link to technical details for the signal?
When I connect the multi-meter directly to the signal, it reads 0V or 5V. Connected to FiO0/GND, it reads 3.35V or 5V. I'm using http://www.watlow.com/F4T.cfm (See the digital I/O module under the F4T user guide: installation & troubleshooting).
Looking at page 22 of the F4T user guide it does not look like it has push-pull (5V/0V) digital outputs. Rather it has NPN or PNP outputs:
https://labjack.com/support/app-notes/open-collector-signals
From what you describe in your case it sounds like the output is switching between 5V and open (high-impedance) which would be PNP. Try adding a 4.7k pull-down from FIO0 to GND which will hold FIO0 low when your signal is high-impedance.