Does HDMI carry digital video and digital audio simultaneously, or do I need a separate digital audio cable?

If I want to connect a DVD player digitally, would I need two separate cables? For example, an HDMI cable for video and a digital coax cable for audio?
Update: So will I get the full digital surround sound experience by connecting an upscaling DVD player (with HDMI output) and an HD DVR (also with HDMI output) to my Denon AVR-588 receiver? Then using the receiver's HDMI output to connect to the TV and using the receiver's speakers terminals for the surround sound?
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