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Definition
Audio bit depth determines the number of possible amplitude values for each sample. 16-bit audio (CD standard) provides 65,536 levels with about 96 dB of dynamic range. 24-bit audio provides 16.7 million levels with 144 dB of dynamic range, used in professional recording.
Each audio sample is stored as a number representing the sound wave's amplitude at that moment. The bit depth determines how many distinct values are available. With 16 bits, there are 2^16 = 65,536 possible values, giving about 96 dB of dynamic range — the difference between the quietest and loudest sounds that can be represented without distortion.
24-bit audio provides 2^24 = 16,777,216 levels and about 144 dB of dynamic range. This extra headroom is valuable during recording and mixing because it provides a larger safety margin against clipping (distortion from exceeding the maximum level). For the final consumer format, 16-bit is more than sufficient for any playback system.
The debate between 16-bit and 24-bit for listening is largely settled: in controlled tests, listeners cannot reliably distinguish between properly mastered 16-bit and 24-bit audio. The human ear's dynamic range is about 120 dB in ideal conditions, and most listening environments have ambient noise that reduces effective dynamic range well below 96 dB. 24-bit is for production; 16-bit is for delivery.