Each additional bit of resolution adds approximately 6 dB of dynamic range

The dynamic range of a PCM digital audio system is determined by how many bits represent each sample. The relationship is: maximum dynamic range (dB) ≈ number of bits × 6.11 (in practice, 6 dB is used). This arises because each bit doubles the number of quantisation levels, corresponding to a factor-of-2 amplitude ratio, which is 6.02 dB. An 8-bit system offers ~48 dB of dynamic range (worse than analog tape), 16-bit gives ~96 dB (CD quality), and 24-bit provides ~144 dB. This principle explains why professional recording uses 24-bit—the extra bits provide headroom for signal peaks without sacrificing resolution in quiet passages.

Examples

16-bit audio: 16 × 6.11 ≈ 98 dB dynamic range—sufficient for most music. 8-bit audio: only ~48 dB, so soft sounds vanish into quantisation noise. 24-bit: ~146 dB, exceeding the range of human hearing.

Assessment

A recording is made at 16-bit/44.1 kHz. Calculate the theoretical maximum dynamic range. Then state how many bits would be needed to match the 120 dB range of the human ear.