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Analog-to-Digital Converter (ADC)

Why an ADC Is Needed​

A sensor measures a physical quantity (temperature, light, pressure, etc.) and outputs a proportional analog signal, usually a continuous voltage. A microcontroller or a Raspberry Pi can only process digital values. Many boards (for example the Raspberry Pi) have no analog input at all and would only ever read 0 or 1.

An analog-to-digital converter (ADC) bridges this gap: it samples the analog voltage and encodes it as a digital number. The result is then transferred to the controller, often over a bus such as I²C.

Resolution and Quantization Steps​

The resolution of an ADC is given in bits. The number of bits determines how many distinct digital values (quantization steps) the converter can output:

Number of steps = 2^n        (n = resolution in bits)
  • 8-bit => 2^8 = 256 steps
  • 10-bit => 2^10 = 1024 steps
  • 16-bit => 2^16 = 65536 steps

More bits means a finer division of the input range and therefore a more precise measurement.

Measurement Resolution (Smallest Detectable Change)​

The measurement resolution is the smallest voltage change that still maps to a different digital value. It is the voltage range divided by the number of steps:

Resolution = voltage range / number of steps

Example: A 10-bit ADC measures a range of 0 V to 10 V.

Steps = 2¹⁰ = 1024 steps
Resolution = 10 V / 1024 steps = 0.009766 V ≈ 9.77 mV

Any change smaller than ~9.77 mV cannot be distinguished by this converter.

From a Measured Value to a Binary Output​

Converting a physical measurement into the ADC's digital output is done in three steps.

Scenario: A temperature sensor covers -20 °C to +80 °C and outputs a proportional voltage of 0 V to 10 V. The ADC has a 10-bit resolution. What binary value corresponds to exactly 25 °C?

Step 1 — Map the measured value to a voltage.

First the voltage per unit is determined, then multiplied by how far the value sits above the minimum:

Voltage span / temperature span = 10 V / 100 °C = 0.1 V per °C

25 °C is 45 °C above the minimum of -20 °C
U = 45 °C x 0.1 V = 4.5 V

Step 2 — Convert the voltage to a digital value.

Digital value = (U / voltage range) x number of steps
Digital value = (4.5 V / 10 V) x 1024 = 460.8 ≈ 461

The result is rounded to the nearest whole step, since the output can only be an integer.

Step 3 — Express the value in binary.

461 = 0001 1100 1101
info

Some textbooks divide by 2^n - 1 (here 1023) instead of 2^n (1024), so that the maximum input maps exactly to the highest code. Both conventions appear in practice; the difference is negligible at higher resolutions. This page uses 2^n to match the step count.

See Also​