I would guess that the issue you have is in the software setup that the others have shown and likely will help.
In the even that it is an issue in how it is hooked up, I have been down that patch. My 7870 only had DVI and RGB ports.
If your 7870 is a model without HDMI. Then it will have DVI with Audio Pass Through. You can then get a DVI HDMI adaptor. Buy one that says it is AMD or ATI compatible if possible. You could message AMD support and see if they have them available or the support department of your cards maker. For instance XFX sent me on just for the asking some years back. Either say support may know exactly the model to look for regardless if needed.
I originally ordered one and then another that did not work. Did some digging and found out it matters what kind. That was when I contacted my card maker XFX.
Just wanted to share in case it is relevant now or in the future.