HDMI not showing up in audio playback devices

Hello,

I seem to be having some problems with the digital audio playback using my hdmi cord. I have three of them and none of them seem to be working. In the past when I've had this problem I've done what anyone would do, gone to playback devices and set HMDI as default, but the problem is. . . . it's not showing up there or anywhere else. I've tried refreshing device output, I've looked everywhere that I possibly could to try to find where the output is hiding and it is just not there.... anyone wanna help me?