Nope - the box you have will work just fine with your TV at HD-quality.
I don't think Cox has any boxes that will do 4k. You may want to call them and see if they do and then exchange your existing box with the 4k one. But in all you only need one box.
The cox box will do 1080p which is the best image quality for hd. To get 4k material you need to hook up another device. On gooh buy is thr new xbox which includes a 4k blueray player for little more than just a player. It also can stream amazon orime and youtube 4k material.
I don't believe you do. I think the Cox service will deliver 1080 HD but anything beyond that is unlikely. I certainly haven't seen a 4k box advertized
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