How does a converter choose a binary number for a voltage?

A digital system cannot store every possible analog voltage as a distinct finite binary number. An analog-to-digital converter assigns each sampled voltage to one of a limited set of codes. A successive-approximation converter makes that choice through a sequence of comparisons, narrowing the possible range one bit at a time.

First, a sample-and-hold circuit captures the input voltage closely enough that it remains stable during the conversion. A digital-to-analog converter inside the device generates a trial voltage from a trial code. A comparator then indicates whether the held input is above or below that trial. This is a physical comparison of voltages, not a computer guessing from an already known digital answer.

Consider a simplified three-bit converter with a 0-to-8-volt range and eight one-volt code intervals. For an input of 5.3 volts, the first trial is 4 volts, corresponding to the most significant bit. The input is higher, so that bit is kept. The next trial is 6 volts; the input is lower, so the next bit is cleared. The final trial is 5 volts; that bit is kept. The result is binary 101, identifying the interval from 5 up to 6 volts in this teaching convention.

The output does not preserve the exact 5.3-volt value. Every input within that interval receives the same code. Increasing bit depth provides more, narrower intervals across the same full-scale range. However, resolution is not the same as accuracy. Reference-voltage errors, comparator offsets, electrical noise and nonuniform code transitions can limit how trustworthy the result is. An input beyond the allowed range may simply produce the highest or lowest code, concealing how far outside it lies.

Sampling chooses when a signal is observed; quantization assigns a finite code to its value. More bits cannot repair an insufficient sampling rate, and more samples cannot fix an inaccurate voltage reference. The held voltage and internal trial voltages must also settle adequately. Within these conditions, each comparison narrows the remaining range, so an ideal n-bit successive-approximation conversion takes n bit trials after acquisition. The final code is a statement about an interval, not a perfectly exact copy of the analog voltage.