Just got a HD tv, know nothing. Can I run the standard coax cable to my tv and watch HD channels in hi def?

I've been all over the web and the answers are conflicting. Some say you must have a HD converter box and run HDMI cables to the tv for the resolution to be 1080p, others say you can watch the hi def from coax. Again, my simple question is, "Will standard coax allow you to watch in 1080p, if the... show more I've been all over the web and the answers are conflicting. Some say you must have a HD converter box and run HDMI cables to the tv for the resolution to be 1080p, others say you can watch the hi def from coax. Again, my simple question is, "Will standard coax allow you to watch in 1080p, if the transmission is 1080p?" Thanks
Update: I've been all over the web and the answers are conflicting. Some say you must have a HD converter box and run HDMI cables to the tv for the resolution to be 1080p, others say you can watch the hi def from coax. Again, my simple question is, "Will standard coax allow you to watch in 1080p, if the... show more I've been all over the web and the answers are conflicting. Some say you must have a HD converter box and run HDMI cables to the tv for the resolution to be 1080p, others say you can watch the hi def from coax. Again, my simple question is, "Will standard coax allow you to watch in 1080p, if the transmission is 1080p?" Thanks

Edit - Thanks for all the great answers! Wish I had come here first. Too much good info. to choose a "best."
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