Some of the confusing aspects of digital recording is whether to select 32-bit float over 24-bit as the resolution for recording. There are recordings software that supports both 32-bit float and 24-bit depth (for example Audacity and Sony Sound forge). There are also recording software that does not have 24-bit but only offers 32-bit float recording as an equivalent of 24-bit recording (for example Adobe Audition). There is a lot of questions behind this topic that beginners would like to ask, for example:
1.) Is 32-bit “float” the same as 32-bit recording?
The answer is no. 32-bit recording is 32-bits fixed point (not using float system) while a 32-bit float has a 24-bit resolution with additional 8 bits for headroom/dynamic range. For example Sony Sound forge differentiates these two clearly when you are creating a new recording project (File – New); see screenshot:
Sony Sound forge 32 bit recording
The 32-bit (IEEE float) is the 32-bit float bit depth.
2.) Is 32-bit float in recording software is essentially the same as 24-bit recording?
Yes. For example in Adobe Audition, you cannot directly set a 24-bit depth recording. Instead they have a 32-bit float. After converting analog to digital data using your audio interface (for example sound card); Adobe Audition will be storing these recordings in 32-bit float format in your computer hard disk drive but the resolution is still 24-bits. To get the most quality out of your recordings, set your audio interface to record at the highest supported bit depth (which should be 24-bits and NOT 16-bit). As of this time, 32-bit sound cards are not commercially available; however most decent sound cards and audio interfaces now support 24-bit depth resolution during recording.
In the ADC (Analog to digital converter), the analog audio is sampled at 24-bits (if configured at this bit depth). The output of the ADC is then feed to Adobe Audition (or other recording software if configured to record at 32-bit float) which will be storing digital information in 32-bit float format instead of pure 24-bits. You can visualize it as follows:
signal path of 32-bit float recording
What is a 32-bit floating system and how it works?
One of the most common 32-bit floating system format used is the IEEE 754-1985. It is why you commonly see the abbreviation (IEEE) besides the 32-bit specification. This signifies it is using a floating point system. Below is how the 32-bit floating system is organized:
32 bit floating structure
It consists of a sign (which tells whether the value is negative or positive); an 8-bit exponent and a 23-bit mantissa. During digital audio processing (effect plug-ins, etc); the recording/mixing software will do intensive and complex numerical calculations internally. With 32-bit float, the result of calculations during effect processing will not result to truncations or rounding errors of digital data because complex results can be represented by the 32-bit floating binary. It is the reason why most digital audio workstation software works internally at 32-bit float to get the best quality out of effects processing and mixing. To understand the conversion process between 32-bit float to decimal, download this 32 bit float to decimal Excel calculator.
Using the spreadsheet, a 32-bit digital audio data such as:
10111110010110000000000000000000 is equivalent to -0.2109375.
32 bit example calculation to decimal
Converting 32-bit float binary to decimal is using this formula:
[(-1) ^sign] x 1.mantissa x 2^ (exponent -127)
Using the above example:
a.) The sign is (-1) ^1 or -1.
b.) The mantissa is the fraction part in binary. In the above example, this is the mantissa: 10110000000000000000000
Converting the binary fraction to decimal:
(1 x 2^-1) + (0 x 2^-2) + (1 x 2^-3) + (1 x 2^-4) + 0…0 = 0.6875
c.) The exponent section is 01111100, the decimal equivalent is:
(0 x 2^0) + (0 x 2^1) + (1 x 2^2) + (1 x 2^3) + (1 x 2^4) + (1 x 2^5) + (1 x 2^6) + (0 x 2^7) = 124
Using the above values to compute the decimal equivalent with the provided formulas:
(-1) x (1.6875) x [2^ (124-127)] = -0.2109375
What will happen in the analog to digital conversion is opposite. Given the decimal analog equivalent, the recording software will compute the 32-bit float binary equivalent.
Advantages of Recording/Mixing at 32-bit float bit depth over 24-bit
If you have utilized the maximum bit depth recording capability of your audio interface (such as a soundcard), you will be recording at 24-bits. The digitized signal only has 24-bit resolution; however adding extra 8-bits will provide additional headroom and dynamic range to your digital signal with the following benefits:
1.) 32-bit audio allows processing of signals above 0dBFS “internally” without clipping in the digital domain. It is because of increased headroom or dynamic range. “Internally” means within your DAW (digital audio workstation software).For example in Cubase manual; it recommends projects to be recorded in 32-bit float format for two obvious reasons:
a.) Prevent digital distortion and clipping during tracking.
b.) Cubase internal audio processing is in 32-bit float (like most DAW) and tracking in 32-bit float means that the recorded quality will be intact /untouched (because it is also in 32-bit float). If you are using below 32-bit float, possible audio degradation will occur.
2.) While you prevent high possibility of clipping with 32-bit float, you have the same signal to noise ratio (SNR) as the 24-bit audio.
Max SNR = 6 x bit depth used during recording
So a 16-bit recording has a maximum SNR of 6 x 16= 96dB. Below are the maximum SNR of 24-bit audio and 32-bit float resolution:
Max SNR of 24-bit = 6 x 24 = 144dB
Max SNR of 32-bit float = 6 x 24 bits (removing those extra 8 bits) = 144dB.
Take note that recording at 32-bit float will result to large file sizes for your recording track which can be a downside if you have limited hard disk drive spaces. The file size is computed using this formula:
File size of your digital audio in bytes = [(sampling rate) x (bit depth) x (number of channels) x (seconds)] / 8
So a digital recording of 10 seconds audio sampled at 32-bit float/96KHz stereo would have a file size of:
File size = [(96000) x (32) x (2) x (10)]/8 = 7,680,000 bytes or approximately 7.7 MB
With pure 24-bit recording, the file size would only be: 5.76MB, so a 32-bit float audio would be around 34% larger.
Content last updated on July 5, 2012