PCM (Pulse Code Modulation)
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One of the biggest applications of digital logic is using circuits to perform arithmetical operations. While theoretically, any number system could be used, binary is the most simple to express in terms of digital logic circuits.
Digital electronics devices handle numbers in the form of the binary system. That is, the numbers are represented in base-2, with only two digits. That way, when a digit comes along, it's much easier for the electronic device to decide what digit it is.
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Fourier analysis is used in many places. Three examples are digital filtering, where a signal is converted to frequency domain, certain bands are removed or processed, and then converted back to time domain; your cell phone or its headset, if it has advanced noise cancellation technology; and the telephone system itself, where digital filtering is used to minimize bandwidth demands.