Most of the circuits we have seen thus far have dealt with analog signals that take on continuous values within a certain range. There is, however, a broad domain of electronics in which signals take on only discrete values and can therefore be represented by integers. The dots and dashes in the Morse code, or the presence or absence of a requirement for a decision, are straightforward examples of such digital signals.

Electronic devices with two well-defined states arise much more naturally than devices with ten states; for this reason, digital signals are represented and processed in binary form rather than in the familiar decimal form; that is, counting is done by twos rather than by tens. It turns out furthermore that a binary representation, while not optimal—counting by threes would in fact be better—results in simpler circuits.

Digital circuits are mandatory for the logic and arithmetic functions inherent in computers, but they are also used for other purposes. Much use is made, for example, of the fact that digital signals are large compared with most analog signals (volts rather than microvolts) and therefore far easier to separate from noise. Analog signals converted into digital form (that is, into a series of integers) lose virtually no information if the sampling resolution and the sampling rate are high enough, and transmission of the digitized signals over noisy channels is often perfect. How much can be gained by such procedures ...

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