DVI is a digital connection and the best you can use. HDMI uses the same signaling as DVI except it includes audio channels. AFAIK, no computer monitor uses HDMI yet, only TVs. If you want to hook to a DVI monitor, you need the mini-DVI to DVI adaptor. To connect to an HDMI TV, you need the same adaptor plus a DVI to HDMI adaptor.
Steve