How Do Digital Multimeters Measure Voltage, Current, and Resistance?

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How exactly do digital multimeters measure things like potential difference, electric current, and electrical resistance?
 
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They really only sense voltage. They measure current by putting the current through a small resistor and measuring the voltage across it.

They measure the voltage with an analog-digital-converter (ADC), there are a few different types but basically they are a source of different fixed voltages and a an amplifier to compare each fixed voltage with the measured voltage until they are are equal - then use that number.