Quantization Signal-to-Noise Ratio

Rounding a continuous voltage to the nearest of $2^n$ levels throws away whatever fell between them, and the discarded remainder behaves like added noise. Work out its power for a full-scale sine wave and you get $\mathit{SNR} = 6.02n + 1.76$ dB. Sixteen bits gives $96.32 + 1.76 = 98.08$ dB, which is the dynamic-range figure printed on every CD-era datasheet.

The useful form of this is the slope. Each extra bit halves the step size, which quarters the noise power, which is 6.02 dB. One bit, six decibels, always. That single fact lets you do converter arithmetic in your head: 8 bits is about 50 dB, 12 bits about 74 dB, 24 bits about 146 dB, and the last of those is well beyond what any analogue front end can actually deliver, which is why 24-bit audio buys less than it advertises. The odd-looking 1.76 dB is $10\log_{10}(1.5)$ and comes purely from the crest factor of a sine wave, so it is not a property of the converter at all.

The mistake is comparing this number to a measured one without noticing the signal level. The formula assumes a full-scale input. Drive the converter at $-20$ dBFS, as most real recordings sit, and you lose 20 dB of SNR immediately, because the noise floor is fixed by the step size while the signal has shrunk. Working converters also fall short of the ideal through thermal noise and nonlinearity, which is why datasheets quote an effective number of bits: measure the real SNR, rearrange this formula, and a 12-bit part often comes back as 10.