Audio Bit Depth
PCM bit depth sets the number of available numerical levels for each sample.
Imagine measuring the height of a waveform with a ruler. A finer ruler gives more possible amplitude values over the same range. Integer PCM bit depth is that amplitude precision; it changes the numerical grid, while sample rate changes the time grid.
With N bits there are 2^N bit patterns. For signed integer PCM, these normally represent values from −2^(N−1) through 2^(N−1)−1. Sixteen bits therefore provide −32,768 through +32,767: 65,536 levels.
Compare the steps, not just the labels
Using a nominal normalized range of −1 to +1, the integer step is 2/2^N. The positive endpoint falls one step below +1 in this convention.
| Integer precision | Levels | Normalized step |
|---|---|---|
| 8-bit | 256 | 0.0078125 |
| 16-bit | 65,536 | About 0.00003052 |
| 24-bit | 16,777,216 | About 0.0000001192 |
Adding one bit doubles the levels and halves the step. Moving from 16 to 24 bits supplies 256 times as many levels, not merely eight more measurements.
Suppose a signal sample should have amplitude 0.001. On the signed 16-bit grid, 0.001 × 32,768 = 32.768, so rounding selects code 33. Reconstructing that code gives 33/32,768 ≈ 0.00100708, an error of about +0.00000708.
On the 24-bit grid, the calculation is 0.001 × 8,388,608 = 8,388.608. Rounding selects 8,389 and gives approximately 0.0010000467. The much smaller step allows a closer result. See quantization error for how such errors behave over a waveform.
Why processing uses extra precision
Even simple volume adjustment can produce values between integer levels. Halving code 33 gives 16.5. If a processor immediately rounds this back to the same integer grid, it loses the fractional part; if it keeps a wider or floating-point working representation, later operations can use it.
Mixing, equalization, and repeated level changes create many such intermediate values. Keeping more precision during processing and rounding at the appropriate final conversion limits avoidable cumulative error. Dither controls the behavior of that last rounding rather than making every sample exact.
Bit depth and the noise floor
Smaller steps can make quantization error smaller relative to the permitted signal range. The often quoted ideal SNR formula, 6.02N + 1.76 dB, describes a full-scale sine and an ideal quantizer with a particular noise model over the full Nyquist bandwidth. It is not a measured dynamic-range guarantee for a microphone, music release, or sound card.
A noisy room, microphone electronics, or earlier processing can dominate long before the numerical limit. A 24-bit recording is useful because it can accommodate precision and recording headroom; it need not contain 24 bits of clean musical detail.
Recognize precision in a media report
A 24-bit sample may occupy a 32-bit storage word. Those spare positions are a storage arrangement, not extra recorded detail. Likewise, 32-bit float uses a significand and exponent, allowing a wide numerical range with different precision behavior from 32-bit integer PCM.
A lossless codec can preserve the encoded integer precision. A lossy codec instead reconstructs an approximation, and its decoder must still choose a working sample format. Consequently, a decoder's float or 32-bit output label and the source's original bit depth describe different stages. PCM sample formats shows how to read those working-format names.