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Hi, Paul. It's easy. Open-drain outputs can be treated just like open-collector outputs. You just need a pullup resistor to the logic power supply.
Assuming you have that power supply available, wire up something like this (view in fixed font or Notepad):
.---------------. .----------------. | Device #1 | ___ | Device #2 | | Vcc o-|___|--. | | | | 1K | | | | | | | Open Drain | | | | | Output | | In o--------o------o | | | | | | | | | | | | | | | | | | Common/GND o---------------o Common/GND | | | | | '---------------' '----------------' created by Andy=B4s ASCII-Circuit v1.24.140803 Beta
Note that the MOSFET will do the exact same thing as connecting the In on Device #1 to GND. The pullup resistor may not be necessary, because Device #1 may have an internal pullup resistor to keep the In at a logic "1" when not active. Or it may have a TTL input which goes to a logic "1" when left floating. But an external pullup is usually used, and probably won't hurt.
This is a best guess based on the information you've provided. It should work, but you really should contact the manufacturer or read the manual on the devices, or provide more information.
Good luck Chris