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?