Hi,
I'd set the inputs with resistive dividers to obtain a high impedance output and in that way not have the device sinking current for nothing/wasting energy pointlessly.
Nice comparator with no phase reversal, by the way, thanks for bringing it to my attention.
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Hi,
Just saw that the TI pdf is about op amps, not comparators - while it's a delightful conversation topic (where does an op amp end and a comparator truly begin, is a comparator just an uncompensated op amp?, etc.) you are not using an op amp I think.
Look at the picture on page 32: op amp voltage follower (internally with some push-pull output stage or other). Now look at any old comparator schematic or typical application and spot the big difference: pull-up resistor (on an open collector output). Op amps are analog and linear input and output (hopefully) whereas the comparator is an analog linear input with a "cheapo" NPN inverter digital output.
All that waffle to explain why I think the ground voltage follower is not a good idea for an unused comparator.