Please help me figure this out….

[JackD201]

All over the net Hi-Rez is being called useless because the focus has been on dynamic range. "You'll never use it" goes the mantra.

So I have been trying to find out if discreet voltage values or rather what and how many voltage steps there are with 16bit and 24bit within say a max output of a paltry 95dB, very usable range.

Are the jumps in assigned values (voltage step sizes) the same or not? Is 24 bit simply a longer tape measure than a 16 bit with the same metrics or at the max length of 16 bit, does 24 have more discreet values on them?

This has been bugging me for years and I can not find a comparative table or chart anywhere.

 

[dmnc02]

All over the net Hi-Rez is being called useless because the focus has been on dynamic range. "You'll never use it" goes the mantra.

So I have been trying to find out if discreet voltage values or rather what and how many voltage steps there are with 16bit and 24bit within say a max output of a paltry 95dB, very usable range.

Are the jumps in assigned values (voltage step sizes) the same or not? Is 24 bit simply a longer tape measure than a 16 bit with the same metrics or at the max length of 16 bit, does 24 have more discreet values on them?

This has been bugging me for years and I can not find a comparative table or chart anywhere.

The way I understand it, more bits mean in principle more discreet values (smaller quantization error). However, this does not take dither into account. Dither reduces quantization error to white noise, so that the net difference is in dynamic range.

 

[Tam Lin]

Dither reduces quantization error to white noise...

Actually, dither increases quantization error to white noise. Quantization noise has a magnitude of 1/2 LSB. TPD dither is 2 LSB. Noise-shaped dither is considerably greater.

You might find this of interest. http://www.stereophile.com/features/705dither/index.html

 

[esldude]

Well 16 bit has 65,535 potential values. The smallest bit is a smaller voltage than the largest.

24 bit has more than 16 million potential values. The first (and largest) 16 bits in a 24 bit signal are the same as those in a 16 bit. You then add 8 bits or 256 steps of smaller sized bits to that to get the 24 bit.

Another example imagine you had your MSB (most significant bit) which is the same size in 16 or 24 bits. If your DAC had a 2 volt max output the value of the MSB would be 1 volt. If you added the LSB (least significant bit), then the size of the 16 bit LSB is 256 times larger than a 24 bit LSB.

 

[dmnc02]

Actually, dither increases quantization error to white noise. Quantization noise has a magnitude of 1/2 LSB. TPD dither is 2 LSB. Noise-shaped dither is considerably greater.

You might find this of interest. http://www.stereophile.com/features/705dither/index.html

"Reduces to" was used as a synonym for "changes to".

 

[JackD201]

Well 16 bit has 65,535 potential values. The smallest bit is a smaller voltage than the largest.

24 bit has more than 16 million potential values. The first (and largest) 16 bits in a 24 bit signal are the same as those in a 16 bit. You then add 8 bits or 256 steps of smaller sized bits to that to get the 24 bit.

Another example imagine you had your MSB (most significant bit) which is the same size in 16 or 24 bits. If your DAC had a 2 volt max output the value of the MSB would be 1 volt. If you added the LSB (least significant bit), then the size of the 16 bit LSB is 256 times larger than a 24 bit LSB.

So 24 bits is just "a longer tape measure"? I was under the impression that for a given reference voltage the LSBv shrinks the more bits you add.

 

[Tam Lin]

"Reduces to" was used as a synonym for "changes to".

Duh; I was just pointing out the irony of your comment. It's a common tactic in digital audio to mask a defect by adding even more noise, aka, dither. Dither may be 'inaudible' but every additional bit occupied by dither is one less bit that represents the signal.

 

[Dre_J]

So 24 bits is just "a longer tape measure"? I was under the impression that for a given reference voltage the LSBv shrinks the more bits you add.

Jack,

Your impression is correct. The tape measure stays the same total length. It just gets divided into smaller chunks.

In the simplest form I can think of at the moment, it would be like a 1ft ruler. Grossly looking at this for concept only, it would be like 16-bits would represent the 12-inch scale where 24-bit would represent that plus the visual gradients between the inches. This is a VERY rough interpretation but it gets the gist of the bit value difference.

I think this hits the core of your question.

However, a bit more talk (no pun intended) about binary representation of numerical values associated 2^16 (65536 ) vs. 2^24 (16777216) would give a reasonable understanding of the same reference voltage divided into the available steps. So the voltage step size does shrink based on the available bit (16 vs 24) representation of the reference voltage.


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To your other comment on dynamic range: you can't get more output than the reference maximum but the gradients between the steps yields much more useful step size. I'm not going to get pulled into a discussion on the merits other than to say I'll take 24-bits if I can get it over 16-bits if it's real.

Dre

 

[JackD201]

Thanks Dre. When I was looking at formulae for LSBv the number of bits were in the divisor.

 

[esldude]

So 24 bits is just "a longer tape measure"? I was under the impression that for a given reference voltage the LSBv shrinks the more bits you add.

I think other replies have answered your question. I explained it badly.

You are correct the voltage of the LSB shrinks with more bits.

The MSB is half the max voltage and each subsequently smaller bit is half of the one above.

I bungled the explanation, but when I said the first 16 bits are the same size, I didn't intend each bit is the same. Just that the 16th bit in a 16 bit signal is the same size as the 16th bit in a 24 bit signal. The 15th bit is the same in both too, but 15th bit is twice the voltage of the 16th bit. The 17th bit in a 24 bit signal is half the size of the 16th bit and smaller than is represented in a 16 bit system.

 

[Vincent Kars]

This is how I understand bit depth.
0 dBFS is the loudest signal a DAC can produce.
Each bit is approximately 6 dB.
With 16 bits you can go down to -96 dBFS
With 24 this will be -144 dBFS
24 allows for the tiny details below -96.
Indeed the first 16 bits are the same, the next 8 of the 24 yields a smaller step size, theoretical 256 discrete staps but in practice less as no AD/DA converter can resolve -144 dBFS