A "digital" volume control does not have to be implemented by "throwing away bits". If you were to "throw away" a bit, and I guess that means left shift the data, the bit you would lose would be the least significant one, which, since you are listening at reduced volume is unlikely to be audible. But such a shift would give a 6dB volume reduction, so I doubt that such an approach is used.
CD player connected directly to Amplifier?
I've been noticing some CD players which can be connected directly to the amp; in many models, its the recommended way to play them. I've never done this, but it seems like a good way to go assuming one has a nice high-end cd player equipped for such a task. I see the obvious advantage of foregoing the expense of a separate preamp, especially in a combined HT/2 channel rig like my own. Is there an obvious advantage in performance? Anyone have any thoughts or experience with this method?