1.3 Data Representation in a Computer System
Computers represent data using 0's and 1's, also known as binary numbers. Why do computers use binary notation instead of the more familiar decimal notation (using digits 0-9) that people use? Each digit, whether binary or decimal, must be represented by a voltage in the computer's circuitry. It is easy to build circuits that discriminate between two voltages. We could call these voltages "on" and "off." It is much harder, though not impossible, to build circuits to discriminate reliably among ten different voltages.
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Assessments:
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1.3.1 Bits and Bytes
Data Representation Using Binary Digits
Increasing Need for Bytes
Data Representation Using Binary Digits
A piece of data, such as an alphabet letter, may be represented using a sequence of binary digits- 0's and 1's. There are several types of codes used to represent character data. For example, using extended ASCII (America Standard Code for Information Interchange) code, the alphabet letter "a" can be represented using a series of eight binary digits, "01100001." Each binary digit is called a bit. And, eight bits is one byte. Extended ASCII code uses eight bits (or one byte) to represent input characters. Below are binary representations of characters in extended ASCII code.
Figure 1 ASCII code
All data, including audio, visual, and program instruction data can be represented and stored using a sequence of binary digits, or a sequence of bytes. Recall that a file is a collection of data. In some files, the bits of data directly encode individual letters, numbers, and punctuation symbols that make up words and sentences. In other files such as an image file, the bits of data need to be computed in order for them to transform to images that we can interpret.
Most applications such as Microsoft Word or PowerPoint encode information in specialized ways that are not readable by humans. Thus, even though Microsoft Word is often used to edit text, a Word document cannot be properly displayed by a simple text editor like Notepad because the document includes information in a format specific to Microsoft Word. Therefore, it must be opened by Microsoft Word to be read. Some files have a header section that indicates which format was used to encode the data in order to allow the computer to reassemble the binary data back into the human-readable form of the document.
Increasing Need for Bytes
In the late 1970s and early 1980s, inexpensive personal computers were manufactured for the first time, and soon a large consumer market developed. At first small amounts of memory such as thousands of bytes were all that was needed to handle the simple spreadsheet and word processing tasks. But, before long, users wanted software to allow them to do more tasks such as creating drawings and generating complex page layouts. As consumer demand grew, computing requirements also grew. This demand led to new developments that expanded memory capacities. By the mid 1980s, memory was up to millions of bytes. Today, office and home computers often have billions of bytes in memory capacity. Memory for data-intensive systems, such as the Geographic Information System (GIS), require trillions of bytes. Below is a chart illustrating the storage capacity over the years since the 1970s with their associated prefix and abbreviation.
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Decade |
1970s |
1980s |
1990s |
2000s |
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Order of magnitude in Storage capacity |
Thousands |
Millions |
Billions |
Trillions |
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Prefix |
Kilo (103) |
Mega (106) |
Giga (109) |
Tera (1012) |
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Abbreviation |
K |
M |
G |
T |
In terms of storage, more is better—which means more information in the form of both data and programs that act on that data can be stored. Corresponding to the growth in storage capacity, memory capacity is also increasing. Moreover, memory technologies are getting smaller, lighter, and faster, for about the same price. You will learn more about storage and memory technologies in the next unit of this course.
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