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2: Codes

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    50156

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    In the previous chapter we examined the fundamental unit of information, the bit, and its various abstract representations: the Boolean bit (with its associated Boolean algebra and realization in combinational logic circuits), the control bit, the quantum bit, and the classical bit.

    A single bit is useful if exactly two answers to a question are possible. Examples include the result of a coin toss (heads or tails), the gender of a person (male or female), the verdict of a jury (guilty or not guilty), and the truth of an assertion (true or false). Most situations in life are more complicated. This chapter concerns ways in which complex objects can be represented not by a single bit, but by arrays of bits.

    It is convenient to focus on a very simple model of a system, shown in Figure 2.1, in which the input is one of a predetermined set of objects, or “symbols,” the identity of the particular symbol chosen is encoded in an array of bits, these bits are transmitted through space or time, and then are decoded at a later time or in a different place to determine which symbol was originally chosen. In later chapters we will augment this model to deal with issues of robustness and efficiency.

    Screen Shot 2021-04-24 at 6.20.13 PM.png
    Figure 2.1: Simple model of a communication system

    In this chapter we will look into several aspects of the design of codes, and show some examples in which these aspects were either done well or not so well. Individual sections will describe codes that illustrate the important points. Some objects for which codes may be needed include:

    • Letters: BCD, EBCDIC, ASCII, Unicode, Morse Code
    • Integers: Binary, Gray, 2’s complement
    • Numbers: Floating-Point
    • Proteins: Genetic Code
    • Telephones: NANP, International codes
    • Hosts: Ethernet, IP Addresses, Domain names
    • Images: TIFF, GIF, and JPEG
    • Audio: MP3
    • Video: MPEG

    This page titled 2: Codes is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Paul Penfield, Jr. (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.