A 24bit digital format doesn't mean the DAC actually has 24bit of SNR. Hell, most DACs in computers, phones and the like struggle with producing 16 bits. Not to mention that even if you had that headroom, when approaching the threshold of hearing would mean that you wouldn't be able to tell a difference at lower volumes.
assuming a signal is played at "normal" listening volume after first being attenuated by 1/8 digitally (samples shifted 3bits down) and then passed through a high quality dac and amplified, are you saying the difference between 16 and 24 bit streams would be inaudible or nearly so? That to me sounds surprising. That seems to imply that the difference to playing the 16 bit stream unscaled (No digital attenuation and 8x on the analog side) would also not be hearable?
Well, depending on the gain of the monitors, it will not matter With low enough gain you will have enough headroom, with high gain you run into hissing from the source. At a high gain the hissing from the DAC's noisefloor will be dominant, making the loss of bits a thing of minor conern. In any case, with powered monitors you need an analog volume control at the end of the chain, that's the correct practice if you care about quality.
Yes there is an analog gain but since volume is controlled by digital attenuation, the analog gain is set to the maximum listening level, which is rarely used.
The ideal solution would be a digital format where desired attenuation is passed along to the amp, but I don't think eg Toslink does that.
So yes if you want single device (phone) control over volume then you attenuate and amplify a noisier signal only for the convenience of not having to use dual volume controls. It's less than optimal, but like I said, I think there aren't any good digital audio standard with attn.?
So while you do amplify noise, surely you don't want to also lose range? Even if the noise dominates, the DR can easily be avoided!
