To connect your Nexus 7 FHD to your TV or monitor using an HDMI cable, you need a Slimport cable that you connect in the micro USB port of your Nexus 7 FHD on one end, and to your HDMI cable on the other hand. Do NOT buy a cheaper MHL cable which will not work; I had a couple of those at home for other devices and none of them worked with the Nexus 7 FHD.
Some people report prices above $50 in some cases for a Slimport / Micro USB cable, so decided to look into it and found much more affordable alternatives like this Slimport MyDP Micro USB to HDMI HDTV for under $13 including free shipping and taxes.
I have received and tested this cable with my Nexus 7 FHD, so I recommend it. Beware it takes a while for the Nexus 7 to start outputting video when you first connect the cable (took me over one minute the first time).
If you find a working and even cheaper alternative, please let me know.