Volume control on DVD player remote. Lose resolution at low volume?

[Circlotron]

My DVD player that I can’t shut up about has a volume control on the remote. What I was wondering was how would it achieve control of the volume? Inside the player is mostly a BIG chip, a 24 bit d/a and an output opamp. Would the big chip just do scaling tricks to the audio bitstream to make the sound quieter and therefore we lose resolution as the volume is turned down because we are effectively using less bits of the 16 bit source resolution? Or would it do it the smart way and allow the bottom 8 bits of the 24 bit d/a to come into action so we still get the full 16 bit resolution but all the bits are right-shifted somewhat?

[tiefbassuebertr]

Often overlooked, the need to distinguish between digital volume control (digital attenuator) and digital controlled volume control (digital controlled attenuator).
The first kind seems to be in use by your DVD device.
The second is a better way; here, the term "digital" means only the kind of the resistance switching select (already after digital-analog converting) for the degree of attenuation without losses of the signal resolution.

[SoNic_real_one]

Both of them will reduce the final resolution.
Digitally by truncating the PCM and therefore the DAC will output a smaller singnal (lower SNR/Dynamic range).
Analogic by lowering the signal at some point after DAC, lowers the SNR/Dynamic range.
Distortion levels might be sligthy better in the second case, but that depends of the DAC linearity.