HIFI Diary: Demystifying Bit Depth – What Exactly Are 1-bit, 16-bit, and 32-bit Float?

Sampling precision, also known as bit depth, has a straightforward definition online. Baidu Baike introduces it as follows:

Sampling precision digitizes the amplitude axis of an analog signal, determining the dynamic range of the analog signal once digitized.

And dynamic range refers to:

the logarithm of the ratio between the maximum undistorted output power during audio playback and the system noise output power at rest.

In simple terms, the wider the dynamic range, the more accurate the sound reproduction and the clearer the layering will be. Even at low volumes, you can hear rich, intricate details.

I. An Introduction to 16-bit, 24-bit, and 32-bit

Let us first introduce sampling precision in PCM signals. Common sampling precisions include:

16-bit, 24-bit, 32-bit, and 32-bit float

Taking 16-bit as an example, there are two ways to represent it: in binary, it is represented by 16 bits of 0s or 1s; in decimal, it corresponds to 65,536 (2^16) discrete integer quantization levels. Whether expressed in binary or decimal, it essentially designates the dynamic range of the audio. From an audiophile/HIFI perspective, it indicates the maximum dynamic range this track can record (1 bit ≈ 6.02 dB), which is approximately 96.33 dB (0 dB to -96.33 dB).

From the above, we can draw some common HIFI conclusions:

For example, when digital audio volume is at 0 dB, its sampling precision is completely uncompressed, delivering the maximum dynamic range possible at the current bit depth, and allowing all details to be heard with full integrity.

Having introduced 16-bit, we can directly extrapolate to the Hi-Res standards of 24-bit and 32-bit. Their underlying mathematical logic is identical to 16-bit, as detailed in the table below:

Sampling Precision	Dynamic Range
16bit	0dB~-96.33dB
24bit	0dB~-144.49dB
32bit	0dB~-192.64dB

II. An Introduction to 32-bit Float and 64-bit Float

While the aforementioned 16-bit, 24-bit, and 32-bit formats are primarily used for audio playback, the newer 32-bit float and 64-bit float formats represent an extraordinary new standard for audio recording. “Float” refers to floating-point arithmetic. Taking 32-bit float as an example, in binary calculation, it is computed according to the table below.

Ultimately, 32-bit float achieves a dynamic range that far surpasses standard 32-bit:

Sampling Precision	Dynamic Range
32bit float	-758dB~+770dB (1528dB)

Are you slightly astonished? The 32-bit dynamic range that reigns supreme in the HIFI world does not even reach a fraction of what 32-bit float can achieve. Even more remarkable, 32-bit float can record dynamic range above 0 dB; recording engineers no longer need to meticulously monitor recording levels in fear of a sudden orchestral tutti clipping and distorting the track. Therefore, the emergence of the floating-point standard has vastly elevated the level of live recording, especially in complex acoustic environments. Furthermore, with ongoing advancements in hardware, 64-bit floating-point precision (64-bit float) is also becoming increasingly widespread, and some high-end A/D converters can already output 64-bit float files.

III. An Introduction to 1-bit

After reading about the mind-boggling 32-bit float above, now suddenly encountering 1-bit might feel rather strange to our readers — after all, isn’t this bit depth far too small? In fact, to explain 1-bit sampling precision, we need to understand another concept: DSD (Direct Stream Digital), an audio encoding format distinct from PCM. It is a high-resolution digital audio specification jointly developed by Sony and Philips, announced in 1996, with its initial physical carrier being the well-known SACD (Super Audio CD). Although DSD’s sampling precision is only 1-bit, its base sampling rate reaches a staggering 2.8224 MHz (also denoted as DSD64, meaning 64 times the standard 44.1 kHz sampling rate). Moreover, just like PCM signals, DSD also offers higher specification sampling rates, such as 5.6 MHz / DSD128 and even 11.2 MHz / DSD256. Hence, the 1-bit sampling bit depth does not compromise DSD audio’s actual precision; in fact, DSD64 already rivals 24-bit / 192 kHz PCM files.

Conclusion: With that, the concepts related to sampling precision have been explained. While writing this technical guide, an audiophile friend in our group chat remarked: “I only listen to vinyl; I don’t need to know anything about digital stuff.” At that moment, beyond feeling frustrated, the BLOG owner felt an even deeper sense of sorrow for the HIFI industry. Many audiophiles believe that “subjective listening impression is everything: why talk so much theory, as long as it sounds good, that’s all that matters.” This sentiment has garnered widespread support among numerous enthusiasts, including many “golden ears” and veteran audiophiles. However, few realize that even for vinyl records, the recording and mastering process is largely digital. Just like the 32-bit float introduced above, it was precisely the escalating demands of the recording industry that drove the development of this brand-new technology. We must clearly recognize that technological advancement stems from the demands of target users; without demand, progress naturally ceases. In the BLOG owner’s view, the “as long as it sounds good” attitude causes nothing but harm to the industry as a whole — just like listening to classical music without bothering to understand its historical background, or learning English without studying grammar; objectively speaking, it is merely a form of giving up.

P.S.: In the future, the BLOG owner will continue to select audio-related topics for technical guides. If there is anything you would like to learn about, or if you still have questions regarding this article, feel free to leave a comment, and the BLOG owner will reply when possible.