Chapter 2 Data Representation

Define data types. Visualize how data are stored inside a computer. Understand the differences between text, numbers, images, video, and audio. After reading this chapter, the reader should be able to: O BJECTIVES Work with hexadecimal and octal notations.

DATA TYPES 2.1

Figure 2-1 Different types of data

The computer industry uses the term “multimedia” to define information that contains numbers, text, images, audio, and video. Note:

DATA INSIDE THE COMPUTER DATA INSIDE THE COMPUTER 2.2

Figure 2-2 Bit pattern - a string of bits Bit (Binary Digit)- is the smallest unit of data that can be stored in a computer; it is either 0 or 1.

Figure 2-3 Examples of bit patterns Computer memory does not know that type of data a stored bit pattern represents. It just stores the data as bit patterns. It is the responsibility of I/O devices or programs to interpret a bit pattern as a number, text, or some other type of data.

Data are coded when they enter a computer and decoded when they are presented to the user.

REPRESENTINGDATAREPRESENTINGDATA 2.3

TEXT A piece of text in any language is a sequence of symbols used to represent an idea in that language. Symbols in English language : – Uppercase letters (A~Z) – Lowercase letters (a~z) – Numeric characters (0~9) – Punctuations (., : ; …)

Figure 2-4 Representing symbols using bit patterns

Bit Pattern Length How many bits are needed in a bit pattern to represent a symbol in a language?  It depends on how many symbols are in the set.

Table 2.1 Number of symbols and bit pattern length Number of Symbols Number of Symbols … … 65,536 Bit Pattern Length Bit Pattern Length … 7 8 … 16

Codes Code – Set of bit patterns designed to represent text symbols. Coding – the process of representing symbols

Figure 2-5 Representation of the word “BYTE” in ASCII code ASCII code – developed by ANSI uses 7 bits for each symbol. This means 128 different symbols can be defined by this code.

Extended ASCII To make the size of each pattern 1 byte (8 bits), the ASCII bit patterns are augmented with an extra 0 at the left. Each pattern can easily fit into 1 byte of memory.

EBCDIC & Unicode EBCDIC- – Developed by IBM – Used in IBM mainframe computers. Unicode – – 16 bits (65536 symbols) – Different sections of the code are allocated to symbols from different languages in the world.

Figure 2-6 Image representation methods

Bitmap Graphic A image is divided into a matrix of pixels, where each pixel is a small dot. – More pixels  – Better representation of image  – Better resolution  – More memory Each pixel is assigned a bit pattern. The size and the value of the pattern depend on the image.

Figure 2-7 Bitmap graphic method of a black-and-white image

Figure 2-8 Representation of color pixels Color image Each pixel is decomposed into 3 primary colors: red, green and blue. (RGB) The intensity of each color is measured, and a bit pattern (8 bits) is assigned.

Resolution The term is most often used to describe monitors, printers, and bit-mapped graphic images. Dot-matrix and laser printers, the resolution indicates the number of dots per inch. For example, a 300-dpi (dots per inch) printer is one that is capable of printing 300 distinct dots in a line 1 inch long. This means it can print 90,000 dots per square inch. Graphics monitors, the screen resolution signifies the number of dots (pixels) on the entire screen. For example, a 640-by-480 pixel screen is capable of displaying 640 distinct dots on each of 480 lines, or about 300,000 pixels.

Vector Graphic A image is decomposed into a combination of curves and lines. Each curve or line is represented by a mathematical formula.

Audio Audio is a representation of sound or music. Audio is by nature analog data. It is continuous, not discrete. Audio is converted to digital data and stored in bit patterns. 1. Sampling 2. Quantization 3. Coding 4. Stored

Figure 2-9 Audio representation

Video Video is a representation of images (frames) in time. A movie is a series of frames shown one after another to create the illusion of motion. Today video is normally compressed.

HEXADECIMALNOTATIONHEXADECIMALNOTATION 2.4

A 4-bit pattern can be represented by a hexadecimal digit, and vice versa. Note:

Table 2.2 Hexadecimal digits Bit Pattern Bit Pattern Hex Digit Hex Digit Bit Pattern Bit Pattern Hex Digit Hex Digit A B C D E F

Figure 2-10 Binary to Hexadecimal and Hexadecimal to Binary transformation

Example 1 Show the hexadecimal equivalent of the bit pattern Solution Each group of 4 bits is translated to one hexadecimal digit. The equivalent is xCE2.

Example 2 Show the hexadecimal equivalent of the bit pattern Solution Divide the bit pattern into 4-bit groups (from the right). In this case, add two extra 0s at the left to make the number of bits divisible by 4. So you have , which is translated to x0E2.

Example 3 What is the bit pattern for x24C? Solution Write each hexadecimal digit as its equivalent bit pattern to get

OCTALNOTATIONOCTALNOTATION 2.5

A 3-bit pattern can be represented by an octal digit, and vice versa. Note:

Table 2.3 Octal digits Bit Pattern Bit Pattern Oct Digit Oct Digit Bit Pattern Bit Pattern Oct Digit Oct Digit

Figure 2-11 Binary to Octal and Octal to Binary transformation

Example 4 Show the octal equivalent of the bit pattern Solution Each group of 3 bits is translated to one octal digit. The equivalent is 0562, o562, or

Example 5 Show the octal equivalent of the bit pattern Solution Divide the bit pattern into 3-bit groups (from the right). In this case, add two extra 0s at the left to make the number of bits divisible by 3. So you have , which is translated to

Example 6 What is the bit pattern for 24 8 ? Solution Write each octal digit as its equivalent bit pattern to get