How does the volume control on computer's digital out work?

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I don't understand how a computer controls the volume of its digital outs - both USB and SPDIF / TOSLINK. The only way I can think of for SPDIF / TOSLINK to decrease volume is to compress the signal. For example, if the audio file has 16 bit depth, and I have the volume down half way (on a linear scale), then the signal out from my computer only uses 8 bits. Is this correct?
However, I know that USB ports have their own power for the DAC. So do USB DAC's use the voltage from the USB port to control the volume?
The reason it's relevant is because if my TOSLINK out is compressing the signal, I would want to add an analog volume control to my DAC for best sound quality. Otherwise I can just use my computer to control the volume.
Does anyone know?
 
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Mostly the digital signal is recalculated mathematically by the player, or the operating system. A 16 bit file has about 65000 possible levels. That's chopping it pretty fine and the resulting volume adjustments are also fine.

FWIW, my player (JRiver) does all its volume control in 64 bit, which has an enormous number of possible levels. It is then reduced to 24 bit depth to go out to my EQ and DAC. That still leaves me with over 16 million possible levels. That's a mighty fine slice.

I have tested, measured and listened to 24 bit digital volume control. All I can find is a reduction of S/N, as you would expect. You'll get that with analog volume control, too. I have found no added harmonic or inharmonic distortion, and no FR change. When you have 120dB of S/N in the format, you can afford to throw away a few dB for volume control. My volume control tends to run about 10dB at most. I find that covers almost all the material I own.
 
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You are very welcome!

I would just add that a volume knob can be very handy. Or at least a resistive divider at the amp. You don't want to do too much attenuation in the digital realm, simply because you are now driving the DAC and its output stage down into the noise floor. I've found 10dB for general use to be just fine. 30dB would be excessive, IMO. You may want to look at what your digital attenuation tends to be, and if it's too much, reduce the gain some at the amp. That way you can keep your digital volume control within about a 12dB range. I've found that to be plenty to cover a wide range of recordings.
 
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