The volume control in digital processors (or CD players) can be implemented in the analog or the digital domain. That is, the analog signal can be put through a standard volume-control knob as is found on a preamplifier, or the volume can be adjusted by performing mathematical operations on the digital data representing the music. Before deciding a digital processor with volume control, you should know the tradeoffs inherent in each approach.
An analog volume control can slightly degrade the signal - no volume control is perfectly transparent - and can introduce small channel balance errors at certain volume settings. For example, when the volume is turned very low, the left channel may be half a dB louder than the right. This situation could reverse as the volume is turned up.
A digital volume control has its own problems. Each 6dB reduction in volume from the maximum setting throws away one bit of resolution. A low volume setting (say, 30dB of attenuation) is equivalent to discarding five bits. If you had true 20-bit resolution in your D/A converter, you'd be listening to 15-bit audio instead of 20-bit. The lower the volume setting, the greater the loss in resolution.
Digital volume control such as DS1669 from Dallas Semiconductor is actually easier and cheaper to implement than analog volume control. Most digital filters have a volume control built-in; the designer need only send a control code to the filter chip to adjust the volume. An analog control requires a potentiometer (the volume control itself), another hole in the chassis, and wiring between the circuit board and potentiometer.