hdmi on mac mini a1176

I'm not sure whether it's progressive or interlaced (1080i or 1080p), but you can get the video signal of HDMI out of it, since it's the same sort of digital signal sent as with DVI.

All you need is a DVI to HDMI adapter, but keep in mind that you won't get any sound of it. For sound you can use the optical toslink outlet (it's in the same connector as the headphone jack).

I've run a configuration like for a couple of years, but had some problems when running Full HD movies because of poor performance in the graphics chip.

It worked just fine while displaying the screen in full resolution though.