Mapman has the right idea. I would slightly reword his statement as follows:
"If all bits in each sample are required to represent a signal at the maximum possible volume, fewer bits will be available to represent each sample at lower volumes."
The higher order (most significant) bits will be fixed in a single state (e.g., 0, as opposed to being able to change between 0 and 1), in order to represent the fact that the signal does not extend above a certain volume.
It should be kept in mind, though, that in concept the loss of resolution with a digital volume control at lower volumes is no different than what occurs with an analog volume control, although there will certainly be differences in degree.
In both cases, the signal level is being reduced relative to the noise "floor" of the parts of the system that are at and "after" the volume control. Simplifying slightly, in the case of a digital volume control the noise floor (referred to as "quantization noise") corresponds to the resolution that is provided by the least significant bit. In the case of an analog volume control the noise floor corresponds to any analog noise that is introduced into the signal path by the circuitry at or after the volume control (noise that is introduced "before" the volume control will be attenuated by the volume control by the same amount as the signal is attenuated, and so the ratio of signal to noise will not change).
In practice, though, noise introduced in the analog signal path following the volume control is usually pretty minimal in a quality system, and the spectral characteristics of analog noise are usually such that the ear can discriminate between the noise and signal levels that are significantly below the noise level. While the 16 bits of the redbook cd standard are significantly less than ideal to begin with, especially considering that two or three of those bits may be thrown away in the recording process to prevent the possibility of clipping the recorder.
Regards,
-- Al
