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The principle of every digital multimeter is based on Analog-to-Digtal conversion ..
In all cases (voltage, current or resistance) digital multimeter always measures voltage ( current measurement is based on voltage measurement across a test resistor, resistor measurement will be done by sending test current through this resistor and measuring voltage across it) ..
For basics (with examples) on A/D conversion have a look at:
Best source of information is the book!
AJ Bouwens, "Digital Instrumentation", Ed. McGraw-Hill.
Its little old book may be out of print but exccelent one on the subject!
Nowadays, an increasing number of electronic measuring instruments are going digital, digital circuitry, digital readout, and digital remote control often being combined in the one instrument. The user of digital equipment has to make the best possible use of the various facilities offered. This book, which deals with these techniques, is divided into three parts. Part 1 "Basic Binary Theory and Logic Circuits," deals with the fundamentals of logic elements. Part 2 "Digital Counters and Timers" discusses the fundamentals of these instruments. Part 3 "Digital Voltmeters and Multimeters," deals with the principle of operation of digital voltmeters (DVMs).