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Analog-to-Digital Converter

Analog-to-Digital Converter

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In short

For an ideal n-bit ADC, digital code = ⌊Vin ÷ Vref × 2ⁿ⌋. A 10-bit ADC with a 5 V reference turns 2.5 V into code 512, with a step (1 LSB) of 4.88 mV.

How it works

Reading an analogue clock is two questions: where is the short hand, and where is the long one.

  1. The short hand gives the hour — read the number it has passed, not the one it is nearest.
  2. The long hand gives the minutes: each number is five minutes, each small mark one minute.
  3. Write it as hours:minutes, then add am or pm — or add 12 to the hour for the 24-hour clock in the afternoon.

The usual mistake is at, say, 2:55: the short hand is almost on 3, but the hour is still 2 until the long hand passes 12.

Examples

Reading the dial:

Analogue to digital
HandsDigitalSpoken
Short past 3, long on 123:00three o'clock
Short between 3 and 4, long on 33:15quarter past three
Short between 7 and 8, long on 67:30half past seven
Short between 9 and 10, long on 99:45quarter to ten
Short between 11 and 12, long on 1111:55five to twelve

For the 24-hour clock, add 12 to any afternoon hour: 3:15 pm is 15:15.

Related: Energy Converter, Power Converter, Frequency Converter.

Analog-to-Digital Converter: frequently asked questions

What is ADC resolution?
The number of bits n, which sets 2ⁿ output levels. A 12-bit ADC has 4,096 levels; with a 3.3 V reference each step is about 0.8 mV.
What is an LSB?
The least significant bit: the smallest voltage change the ADC can resolve, equal to Vref ÷ 2ⁿ.
What is quantization error?
The difference between the actual input and the voltage its digital code represents; for an ideal ADC it is at most 1 LSB (±½ LSB with rounding).