Well, when you turn down the fader the bits are not getting smaller, you are using less of them. The more you turn down the fader the less accurate your signal out becomes. Even though 32-bit mixing engines help minimize this effect this is one of the big reasons digital mixes sound so flat compared to analog mixes.
Try this out for yourself. Record something really hot (careful not to clip). Now try turning the fader in your DAW way down and turn your monitor up to bring it to a decent level. If you ignore all the hiss being generated by doing this you will notice that there is basically no dynamic range. It really brings out the "digitalness" of the sound.
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