Why would the digital optical output from my CD player be louder than that of my streamer?


I thought that a digital output audio signal didn't have volume info encoded in it; ie, that the bit depth tells you the dynamic range of recorded sound, from 0 to highest volume, but does not tell the downstream devices how loud the sound should be (ie, what you actually hear, in SPL).  In other words, the volume would be entirely determined by the preamp (after the DAC converts it from digital to analog), not by the digital output source.
 
But I'm finding that the digital (Toslink) output of my Cambridge CD player is noticeably louder than that of my Bluesound Node, after going thru the same DAC and preamp. Is my assumption of the digital signal having no volume info wrong?
128x128cheeg

I thought that a digital output audio signal didn’t have volume info encoded in it;

For normal stereo this is true, but HDCD and movie soundtrack break this somewhat. Generally not things you need to care about when playing CDs.

The amount of gain applied is entirely up to the device that creates the analog signal.

This also assumes neither player has a volume control. :)

My CD player is louder too. More voltage. Mystery solved.

Not so fast, @hilde45 -- The CD player is sending a digital signal to my DAC/Pre on Optical, and another digital signal to the same DAC/Pre on Coax; for both the volume is the same, but fairly loud.  Now I switch the cables to the Optical and Coax outputs on the Bluesound; again the sound levels are the same, but much less loud. How could higher voltage on the CD player account for that?