32 bit music

[adamdea]

Mostly the second law. It is all tied up with thermal noise and information entropy.

I have done some quick calculations. Assuming an amplifier input with 2V sensitivity into 50K Ohms running at room temperature:

32 bits at 6db/bit is a dynamic range of around 216dB. At full scale (32-bits), the amplifier input current is around 40uA. The current for 1 bit output is 9.3E-15A.

I calculate the Johnson noise current alone at 300K as 8.14E-11A, making just this noise current around 8,700 times greater than the signal.

To make use of 32-bit resolution, you would need to cool the whole of your audio system and your ears to below the temperature of liquid helium.

Don't try this at home!

not wishing to be arsey, but 32*6=192.
This makes me wary of the rest of your calculations. But it seems to be widely accepted that thermal noise in a dac is around -120 dB yielding 20 bits of effective snr. 24 bits is therefore excessive.