quantization
If sampling chops a signal in time, quantization chops it in height. The real voltage can be anything — 1.37294... volts, with endless digits — but a digital number can only take certain fixed values, like the marked lines on a ruler. Quantization is the act of rounding the true voltage to the nearest available level, the nearest line on the ruler. It is the second, unavoidable approximation a converter makes, and it is where a little bit of error is born.
How it works: a converter divides its full-scale voltage range into a fixed number of equal steps. The size of one step is the LSB (least significant bit). For a 0 to 4.096 V converter with 4,096 steps, each step is 4.096 V / 4096 = 1 mV. So a true input of 2.3724 V is read as 2.372 V (level 2372) — the leftover 0.4 mV simply cannot be represented and is discarded. Every reading is therefore off by at most half a step, plus or minus 0.5 mV here. More steps (more bits) make the ruler finer and the rounding error smaller.
Why this matters: quantization sets a hard floor on how faithful a digital reading can be, no matter how clean your analog circuit is. The discarded fraction shows up as quantization noise, and it limits the converter's dynamic range. The key honest point is that this error never fully goes away — you can only make the steps smaller by adding bits, which costs speed, complexity, and money. Choosing the resolution is choosing how much rounding error you can live with.
An 8-bit converter over a 0 to 5 V range has 2^8 = 256 levels, so one step (1 LSB) is 5 V / 256 = 19.5 mV. A true 2.500 V input rounds to the nearest level, 2.500 V (code 128), but a 2.490 V input also reads as code 128 — they are within one step and cannot be told apart.
Rounding a continuous height to the nearest ruler line.
Quantization error is fundamental and permanent — it is not noise from a bad component, it is the price of representing a continuous value with a finite number. Adding bits shrinks it but never eliminates it.