Yosemite not displaying external HDMI monitor at full resolution
1080p = 1920x1080 so you are already getting the highest resolution available on your monitor.

Are you missing the menu bar at the top of the screen and the dock at the bottom? If so, moving the underscan slider beneath the resolution section in the Displays preference pane should resolve your problem.

If you are still having trouble, try a PRAM reset (instructions below). Display resolution settings are stored there.

1.Turn off your computer.

2. Locate Command+Option+P+R keys and be ready to press them simultaneously.

3. Press the power button then immediately press and hold the keys until you hear the startup chime a second time.