HDTV and pc monitor on same video card on 1080p?

hello I have wanted to know if my hdtv would run in 1080p with my other lcd 20" monitor both hooked up to one video card. I have an 8800gt and I currently have a vga cable with a dvi adaptor plugged into my videocard which plugs into the vga port on my HDTV. The problem is the HDTV currently displays 1400 x 1050 at 4:3 aspect ratio with black bars on both ends of the screen and I didnt want to strech the picture out to fit the screen. I wanted to have the HDTV display 1080p at 16:9 aspect ratio at the same time my pc monitor displays 1600 x1000. I was wondering if I bought an HDMI to DVI cable for my HDTV that it would reslove the aspect ratio and resolution on my HDTV.