Practical Effects of Audio Bit Depth?

[Asmodian]

This is a question triggered by a post in the eac3to thread but further discussion of it would be off-topic there.

Originally Posted by Zenitram

They are not. as 0 does not say the same thing as 0.0000 (and yes, quantization bits are similar to float).
I understand this is same for your ears, but it may be different for some compression algorithm and/or for people looking for the count of bits used for quantization (again, zeroes with 16-bit is not same as zeroes with 24-bit, zeroes with 24-bit quantization say that this is more sure that it is silence for real)

It is all about precision information, I understand that you don't care, but that does not mean it is useless for everybody. It is very important for a couple of people I work for.

Is this true in practice? I understand the point of sigfigs when thinking of scientific measurement but I do not believe it applies here. If I feed 24-bit with 0 for the 8 LSBs to a 24-bit DAC do I get different output than if I had fed that same DAC with 16-bit data? Significant figures are not applicable to digital integer formats in that:

1111111111111111, means exactly the same thing as 111111111111111100000000 in a digital integer format.

A DAC would give exactly the same output with either input. A DAC effectively pads any input bit depth below its bit depth with zeros.

I suppose if you understand the ADC very well 16-bit or 24-bit with the 8 LSBs as 0 are different, by a tiny amount. If 24-bit represents 0 to 1, the 16 MSBs represent 0 to 0.99998480 (an error of 0.00152% compared to a 16-bit ADC). However, if you know the ADC used you don't care what the current format is.

This means the ADC and DAC both need to use the same bit depth to avoid quantization errors but truncating to 16 bit or using 24 bits with 8 trailing zeros would both give identical and correct output when using the same DAC. The storage bit depth has no effect on the quantization error at all, only the DAC bit depth compared to the ADC bit depth matters.

Truncating 24-bit with 8 zeros in the LSBs to 16-bit would not cause any additional error, even thinking mathematically, during audio playback.