Dolby 2.0 is just two channel Dolby Digital. DD can be anything from 1.0 up to 5.1.
2.0 can be stereo, or it can be that the two channels are matrix encoded for Pro Logic. Most decoders, when receiving a DD 2.0 source will give you the choice of invoking Pro Logic (or Pro Logic II), or just playing it back un-altered.
Many HD TV broadcasts, as well as some movies via cable and satellite (HBO for example) are in DD 2.0, and should be decoded in Pro Logic.
Right, DD 2.0 is two channel material encoded in Dolby Digital. If done correctly, the bitstream carries three-way information if the two channel is Pro Logic encoded: yes, no or unknown. A decoder should have a four-way setting for this; always on, always off, as indicated (default on) and as indicated (default off).
Burrite, welcome to the forum. The 2 is for 2-channel (stereo). The zero means there is not a discrete LFE-low frequency effect (subwoofer) channel. Just like Dolby 5.1, the .1 is the LFE and the 5 are the five satellite speakers.
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