By converting continuous analog signals into a finite number of discrete states, a process called digitization, then to the extent that the states are suficiently well separated so that noise does create errors, the resulting digital signals allow the following (slightly idealized):
- storage over arbitrary periods of time
- ﬂawless retrieval and reproduction of the stored information
- ﬂawless transmission of the information
Some information is intrinsically digital, so it is natural to process and manipulate it using purely digital techniques. Examples are numbers and words.
The drawback to digitization is that a single analog signal (e.g. a voltage which is a function of time, like a stereo signal) needs many discrete states, or bits, in order to give a satisfactory reproduction. For example, it requires a minimum of 10 bits to determine a voltage at any given time to an accuracy of 0.1%. For transmission, one now requires 10 lines instead of the one original analog line.
The explosion in digital techniques and technology has been made possible by the incredible increase in the density of digital circuitry, its robust performance, its relatively low cost, and its speed. The requirement of using many bits in reproduction is no longer an issue:
The more the better.
This circuitry is based upon the transistor, which can be operated as a switch with two states. Hence, the digital information is intrinsically binary. So in practice, the terms digital and binary are used interchangeably.In the next sections we summarize some conventions for dening the binary states and for doing binary arithmetic