Digital Electronics
The real world is analog (continuous voltage), while processors are digital (discrete numbers). The ADC (Analog-to-Digital Converter) is one direction of the bridge: it turns voltage into a number. The DAC is the reverse: it turns a number back into voltage. An ADC works in two steps: sampling (grab time discretely) and quantization (round the amplitude to the nearest step). Recording a microphone is an ADC job; playing it through a speaker is a DAC job.
Resolution is set by the number of bits: an n-bit ADC divides the range into 2ⁿ steps. 8-bit → 256, 10-bit → 1024, 12-bit → 4096 levels. The smallest step (LSB) is the reference voltage divided by the number of steps: LSB = Vref / 2ⁿ. For example, Vref=5 V, 10-bit → LSB = 5/1024 ≈ 4.9 mV; the ADC cannot see changes smaller than this. This unavoidable rounding error is called quantization noise (≈ ±½ LSB).
The sampling rate has a lower bound: the Nyquist theorem says that to capture a signal correctly you must sample at at least twice its highest frequency (fs > 2·fmax). Sample more slowly and high frequencies appear as low ones — this is called aliasing (like a spinning wheel appearing to turn backward on camera). That is why an anti-aliasing (low-pass) filter is always placed at the ADC input. Audio CDs sample at 44.1 kHz because the ear hears up to ~20 kHz.
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