16 or 24 bits

 

 

8 bit	16 bit	24 bit

Improve the resolution 256 times!

Often pictures are used to demonstrated the difference between high and low resolution audio.
Indeed, the higher the resolution, the sharper the image.
Can we expect the same when moving from 16 bit (CD audio) to 24 bit?
If we look at the numbers, the answer is yes.
16 bit integer allows for 2^16= 65536 different values
24 bit integer has 2^24= 16777216 different values, a 256 times better resolution must make a substantial difference.
Back to the pictures.
If we increase the resolution, the image becomes sharper.
What about a 5000*5000 resolution.
The answer is simple, it won’t fit on the screen.
Whatever the resolution is, the pixels of our screen remain the same size.
In audio more or less the same happens with the bits.

1 bit=6 dB

6.02 to be exact but for convenience sake, let’s use 6.

 

The loudest possible signal in digital audio (all bits are 1) is the reference, this is called 0 dB FS (dB Full Scale).

All other measurements expressed in terms of dBFS will always be less than 0 dB (negative numbers).
16 bits will go down to -96 dB FS and 24 to  -144 dB FS

In essence, 24 bits continue where 16 bits stops. It can record details 16 bits can’t

Noise floor

The theoretical maximum signal-to-noise ratio in an analogue system is around 130dB.

In practice 120 dB is a good value.
You can’t escape thermal noise

 

A couple of specs:

 

Benchmark ADC1 24 bits 192 kHz A/D	THD+N, 1 kHz at -1 dBFS	-102 dBFS, -101 dB, 0.00089%
Benchmark DAC1	THD+N: (w/-3 dBFS input)	-107 dB, 0.00045%
Prism Orpheus AD (line in)	THD+N	-111dB (0.00028%, -0.1dBFS

 

Yes 24 bit can capture those very soft tiny details 16 bit can’t but pretty soon you end in the noise floor of the equipment.

The big debate

You can find many debates on the internet about 16 vs 24
In the pro world this debate has been settled, almost every body is recording with 24 bits today.
They have some very good reasons to do so.

Quantization error

Digital recording is taking samples of the analogue signal.
An integer can only contain natural numbers.
In a integer world 10/2=5 and 9/2=4 or 5 but not 4.5 because you cant store the remainder in a integer. So you have to round the signal you are recording to the nearest integer.
This is called quantization error.
This affect affects the LSB both in 16 and in 24 bits but in case of 24 you are making this error below the noise floor.

Headroom

0 dBFS is the loudest possible signal in the digital domain.
How does this maps to the analogue domain.
Well, it doesn't, it is completely depended on the equipment.

 

When recording, you can’t predict the loudest signal.
Keep some headroom.
There are a couple of standards:

 

BTW: If you are in need of doing some calculations,  go to this page in the Sengpiel site.

 

What ever standard you choose, the consequence is the same, you reserve about 3 bits for headroom. Effectively you are recording with a 16-3=13 or 24-3=21 bits resolution.

DSP

Once the recording is done, the production of the final master can start.
Mixing tracks in the digital domain is again a matter of doing calculations.
Again you profit by having your quantization errors in bit 24 instead of bit 16.

To sum up

24 bits allow for a dynamic rang of 144 dB
You keep 3 bits headroom which leaves you a dynamic range of  126 dB
The theoretical maximum signal-to-noise ratio in an analogue system is around 130dB.

In practice 120 dB is a good value
Your last bit is probably noise in practice so you are effectively recording with 20 bits.
Use the same headroom and 16 bits, you are recording with a 13 bit resolution.

24 bits suffice to capture the full dynamic range of the gear, 16 doesn't.

Playback

What  about playback.
The headroom argument is no longer valid, one knows the maximum level when producing the final master.

 

Noise floor: your gear must have a S/N better than 96 dB otherwise the extra bits 24 offers will be drowned in the noise. But most gear does.

 

DSP: if you use digital volume control or any other kind of DSP, you can profit by using 24 bits (your DAC needs to support this). In case of Redbook audio you can literally chop 8 bits off (48 dB attenuation) without affecting the signal.
Again 24 has the advantage because of the quantization error.

But padding 16 bits audio with 8 bits might do the job too.

The debate continues

Will you hear the difference between 16 and 24?
-96 dB is very soft, can you really hear all those very tiny details below this level?

Audiophiles will probably never reach consensus on any subject:
http://www.head-fi.org/forums/f133/24bit-vs-16bit-myth-exploded-415361/
http://www.hydrogenaudio.org/forums/index.php?showtopic=49843
http://www.audioasylum.com/cgi/vt.mpl?f=pcaudio&m=70002