Moulton Laboratories

the art and science of sound

Is Bits Really Bits

March 2000

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What Really Happens When You Listen To A (you pick the number)-Bit Signal?

First, a quick review. In the digital realm, using our beloved linear pulse code modulation system (LPCM), signal amplitude is represented by a range of binary numbers. The apparent “resolution” of the signal is the ratio between the biggest and smallest numbers in the system. Happily, it is easy to express this resolution in decibels of dynamic range, to wit: each binary bit represents a power of 2 and approximately 6 dB of dynamic range. A 4-bit signal (24, or 16:1) has a dynamic range of 24 dB, while a 16-bit signal (216, or 65,536:1) has a dynamic range of 96 dB and a 24-bit signal (224, or 16,777,216:1) has a dynamic range of 144 dB. You know all this, right? And it’s obvious – 24-bit has way more resolution than 16-bit, right? It has 256 times as much resolution, to be specific. Awesome!

These numbers are abstractions, however, and have no fixed relationship to physical reality. And the way we have implemented the relationship between the virtual and actual worlds leads to not one, but two, BIG problems. So, we need to consider how these ratios are related to the physical world.

First off, these ratios are linked to the analog electronic realm through A/D and D/A converters. Analog signals, of course, are two-dimensional maps of changing energy over time. The maximum amount of energy that can be expressed in any such map is constrained by the limits of the power supply used for that analog circuit, so that the peak-to-peak amplitude of any sine wave cannot exceed the voltage available from the power supply. Skipping over the math, this means that a +/-18 Volt power supply (the most typical case) will yield a maximum signal level of 12.7 Volts RMS or 20.3 dB above 0 VU referenced to +4 dBu.

When we convert that amplitude to binary numbers, the converter is designed so that said amplitude equals the largest signal the digital system can handle. This is a signal that uses ALL of the bits in the digital word (in a 16-bit system, for instance, swinging all the way between 1111111111111111 and 0000000000000000 for positive and negative peaks). We re-name this digital magnitude 0 dB Full Scale (dBFS). This seems like a reasonable and common-sense thing to do. We fix the maximum analog amplitude to equal the maximum digital amplitude. Cool!

But let’s consider what happens at the Least Significant Bit end of the system. In a 16-bit system, the smallest magnitude that can be represented (excluding the effects of dither) is 1/65,000th of the maximum signal, or equal to roughly .2 milliVolts (-72 dBu). When we increase the resolution of the signal to 20 bits, we don’t change the magnitude of 0 dBFS, all we do is push the magnitude of the Least Significant Bit further down toward the grunge and noise floor, so that for a 20-bit word, the LSB is equal to .012 milliVolts. We’ve increased the overall magnitude of the signal by only .18 milliVolts! Going to 24 bits from 16 bits only gains us .2 milliVolts of signal resolution!!

So, we’re increasing resolution at the vanishingly small end of things. No wonder we have trouble hearing it! Increasing resolution in terms of these micro-Voltages makes an increasingly vanishingly small difference. Whew!

Meanwhile, we haven’t bothered to hang on to our “0 dBFS = +20 VU” headroom standard. Instead, we’ve let our nominal level creep upward to as high as –10 dBFS, and sometimes we even master CD pop releases with nominal levels as high as –4 dBFS. In this extreme case our nominal RMS signal level, at the output from a digital console whose electrical specification is that “0 VU = +4 dBu = -20 dBFS”, is a whopping +20 dBu (7.75 Volts RMS)! Hot!!! The implications of this are that (a) we’ve thrown away headroom, and (b) that when we subsequently attenuate this overly hot signal on its way to the loudspeaker (as we most definitely will), we shove those bits even deeper into the analog grunge ‘n noise.

There’s a second problem we have to face as well. We do our listening to acoustic signals, not analog electrical ones. And the relationship between 0 dBFS/+24 dBu electrical levels and X dB SPL acoustical levels is not fixed in any reasonable way. The result has come to be a serious loss of auditory resolution. Consider the following.

If we accept –10 dBFS/+14 dBu as a “nominal” electrical signal level (and we have in practice done almost exactly that), this becomes the level we use to determine the acoustic playback level. For production work, we can assume that level is probably something like 85 dB SPL (it’s the film standard, for instance). That means that the 16-bit noise floor will be at –1 dB SPL, or just below the formally accepted “threshold of audibility” of 0 dB SPL. All well and good, I guess. However, the 20 –bit signal’s noise floor will be at –25 dB SPL and the 24-bit version’s floor will be at –49 dB SPL! Definitely inaudible to us humans. All this is exacerbated by the fact that the acoustical noise floor of the playback room can reasonably be expected to be at or above +40 dB SPL, which means that we can expect masking noises to be running some 90 dB HIGHER than our 24-bit noise floor.

So, we have a serious mismatch of reference levels here, and it unreasonably diminishes any benefit we might expect from the enhanced resolution of 20 or 24-bit digital signals, relative to our venerated 16-bit signal. Failure to reasonably manage the relative headroom of analog and acoustic realms vis-a-vis our digital signal has painted us into a serious wastage of dynamic range. It also means that the resolution benefits of 20-bit and 24-bit signals are not only hard to hear, they’re, well, inaudible as we currently do it. Uh-oh!

Next month we’ll take a similar look at the bandwidth issue. Thanks for listening.

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