## A Question of Bit Depth.

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Reply #8 –

The correct formula is S/N = 6*n + 1.8 dB where n is the number of bits.

The 1.8 comes from the mathematical derivation which I now can't find. However years ago I worked through it and satisfied myself that it is indeed the correct formula. In practical terms 6*n is probably close enough.

If you do a google search for "6n + 1.8" "6n+1.8" etc you will find a few references, not including a derivation unfortunately.

Cheers,

Alan

So you are saying that a 1 bit audio file has 7.8dB dynamic range??? I think not. The correct formula has already been posted by Pio, check it out:

The dynamic range is the level difference (20*log10(level ratio) ) between the quietest sound (1 step peak to peak) and the loudest possible one (2^bitdepht-1 steps peak to peak).

Thus the right formula is

20*log10(2^bitdepht-1).

It gives

Bitdepht / Dynamics

1 bit / 0 db

2 bits / 9.54 db

3 bits / 16.90 db

4 bits / 23.52 db

5 bits / 29.83 db

6 bits / 35.99 db

8 bits / 48.13 db

16 bits / 96.33 db

24 bits / 144.49 db