I think a better solution for what you are trying to do is to use a TV tuner card for your PC. You plug the TV antenna into the tuner, then plug the tuner (via usb or PCI express port normally) into your computer. They come with software to help you record and organize everything which you would normally just be able to watch. Something like this: http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Hauppauge TV Tuners ares great but $$. Also have a look at the AverMedia HD pci card. It has 2 HDMI inputs and a converter (any analog cable you could imagine -> HDMI).
Also, I take it you're gonna want to record tv shows in HD? If that is the case, you're gonna run into HDCP (High-bandwidth Data copy protection). This will prevent you from recording anything through HDMI (can still record TV with component cable). In any case, really research the specific model you wanna get (most legally available tuners have HDCP). If you're ok with component quality, then you're fine. You can record your PS3 or Xbox with HDMI as its not HDCP.
However, there is a driver with a bug still available for the AverMedia tuner that allows 3'rd party software to access the HD stream and therefore record it. I'm not sure if this forum allows discussion of such work-arounds, but if you're interested its driver 126.96.36.199