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Noob question about Bit Depth


It's not a topic directly about FF products so i'm sorry if it doesn't belong here. I'll try anyway.

I was recently told about bit depth that (in PCM16, PCM24, PCM32...), the "steps" were not spaced linear along the dB scale.
For example that it meant that if the audio to quatize was in the lower dB values then the number of steps per dB was less than in the higher values:

To quantize the first 6dB, 0dB to 6dB (-96 dBfs to -90dBfs) you have only 1 possible value,
between 7dB and 12dB (-89dBfs to -83dBfs) you have 2 possible values,
between 13dB and 18dB (-82dBfs to -76dBfs) you have 4 values,
between 18dB and 24dB (-75dBfs to -69dBfs) you have 8 values,
25 and 30 you have 16 possible values
31 and 36, 32 values
between 90 and 96, (-6dBfs to 0dBfs) you'd have 32 768 values.

My calculation is very probably wrong anyway but you get the idea, i guess..
So! I was very surprised by this idea...

I naively thought this was more a linear thing:
In 16 bit you had 65 536 values to quantize, with the same amount of possible values per dB for the 96dB range. (65 536 values divided by 96.33dB of the dynamic range wich gives around 682,667 values per dB)
In 24 bit you'd have 16 777 216 values to quantize with the same number of values per dB for the 144dB range. (16 777 216 values divided by 144.59dB of the dynamic range wich gives 116 508,444 values per dB)

Does anyone can back up one or the other idea ? Or maybe neither of those two... :)
I'd like to understand the general idea.

I hope i'll have an answer here.
Anyway have a good day all !



Hello Thomas,
it is much less complicated.
The A/D-Converter work in linear mode
This means with 16 Bits you have 2^16 - 1 Steps
If your A/D Converter can handle an inputvoltage of 1 Volt this 1 Volt is devided into 65535 Steps
Similar thing with 24 Bits.

dB is also not that complicated but you should know that it is always a relationship (i.e. 20*log10(Outputvoltage/Inputvoltage).

6 dB therefore is a factor of 2.

The calculation is pretty easy

With 8 Bits you get 48dB (8*6)
With 16 Bits you get 96 dB (16*6)
With 24 Bits you get 144 dB (24*6)

Hope that make is clear

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