IndexDigitalDigital Volume & Bit Loss
Digital Volume & Bit Loss
Find how far you can turn a digital volume down before source bits fall off the end.
- Source bits still inside the word
- Bits pushed off the end
- Attenuation
Each square is one bit, most significant on the left. Turning the volume down slides the source to the right.
Input
How it works
Volume as a bit shift
A digital volume control multiplies every sample by a number smaller than one. Halving the level is 6.02 dB, which is the same as moving the whole word one place to the right. An attenuation of decibels therefore moves the signal by
Spare room
If the volume control computes in a wider word than the source, the shifted bits have somewhere to go. Nothing is lost until the shift exceeds the spare width:
A 16-bit source in a 24-bit path can be turned down 48 dB without losing anything; in a 32-bit path, 96 dB.
In practice
The analogue stage of the DAC has its own noise floor, usually 20 to 21 bits below full scale. Bits that fall beneath it are masked by noise whether they are truncated or not. This is why a 32-bit digital volume control in front of a good DAC is transparent at any sensible setting, while a 16-bit one is not.