How to connect MacBook Pro to flatscreen LCD TV?

I have a dvi to hdmi cable, and have connected it, then set the arrangement of my displays on mirror. I have picture, but for some reason I cannot get 1920X1080. Whenever I select this setting the tv shows no signal. Otherwise I still get picture however it does not fill the screen on the right and left side and I cannot see the top bar that shows time and battery and all that.