quantization

After sampling has chopped a continuous signal into discrete moments in time, quantization is the second slice: each sample's voltage gets rounded to the nearest rung on a fixed ladder of allowed values. An N-bit converter has 2^N rungs, so a 12-bit converter offers 4096 of them. Think of weighing yourself on a scale that only reads whole kilograms: your true weight is some smooth number, but the readout has to commit to the closest mark, and the little bit it throws away is gone for good. That discarded remainder is the quantization error.

Because a real signal almost never lands exactly on a rung, every sample carries a small rounding error somewhere between minus half a step and plus half a step. Across a busy signal those errors look random, so they behave like a faint hiss added on top of your audio or data — a noise floor you can never scrub away, only push lower by adding more bits. Each extra bit halves the step size, which is why resolution and noise are two sides of the same coin: the finer the ladder, the quieter the hiss.

Working out the power of that uniform rounding error against a full-scale sine wave gives the famous ideal figure: SNR is about 6.02*N + 1.76 dB. Read it as roughly 6 dB of signal-to-noise headroom per bit. A 16-bit audio converter tops out near 98 dB, a 12-bit data converter near 74 dB — and that is the best case, before real-world thermal noise, jitter, and rung-spacing errors eat into it. So when someone says a converter is 'effectively 11 bits' (ENOB), they mean its real measured SNR matches what an ideal 11-bit quantizer would give.