So, you're connecting your laptop to the TV?
If you know that you have the latest drivers, you will now need to go into the Catalyst Control Centre. The CCC allows you to configure each of your displays individually. Confirm that your TV display in set to 1080.
There should be a setting in CCC called "Overscan", (I cant say where to look for it as I'm not in front of my system) change this setting to zero. When you have changed this setting, test your connection to your TV again, remembering to use that button. on your remote that changes the display from 4:3, Zoom, Widescreen, etc. Using that button change the display to Widescreen.
Then give me some good news, please. :)
If you can't find these settings I'll be in front of my system later.