1. Chapter 2
Data
Representation

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

3. 2.1
DATA TYPES

4. Different types of data
Figure 2-1
Different types of data

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

6. 2.2
DATA INSIDE
THE COMPUTER

7. 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.
Bit pattern- a string of bits
Figure 2-2

8. 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.
Examples of bit patterns
Figure 2-3

9. 2.3
REPRESENTING
DATA

10. 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 (. , : ; …)

11. Representing symbols using bit patterns
Figure 2-4
Representing symbols using bit patterns

12. 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.

13. Table 2.1 Number of symbols and bit pattern length4 8 16 …
128
256
65,536
Bit Pattern Length 1 2 3 4 … 7 8 16

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

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

16. 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.

17. EBCDIC & Unicode EBCDIC- Unicode – 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.

18. Image representation methods
Figure 2-6
Image representation methods

19. Bitmap Graphic
A image is divided into a matrix of pixels, where each pixel is a small dot.
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

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

21. 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.
Representation of color pixels
Figure 2-8

22. 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.

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

24. 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.
Sampling
Quantization
Coding
Stored

25. Figure 2-9
Audio representation

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

27. 2.4
HEXADECIMAL
NOTATION

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

29. Table 2.2 Hexadecimal digits
Bit Pattern
0000
0001
0010
0011
0100
0101
0110
0111
Hex Digit 1 2 3 4 5 6 7
Bit Pattern
1000
1001
1010
1011
1100
1101
1110
1111
Hex Digit 8 9 A B C D E F

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

31. 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.

32. Show the hexadecimal equivalent of the bit pattern 00 1110 0010.
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.

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

34. 2.5
OCTAL
NOTATION

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

36. Table Octal digits
Bit Pattern
000
001
010
011
Oct Digit 1 2 3
Bit Pattern
100
101
110
111
Oct Digit 4 5 6 7

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

38. 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

39. Show the octal equivalent of the bit pattern 1 100 010.
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

40. Write each octal digit as its equivalent bit pattern to get 010 100.
Example 6
What is the bit pattern for 248?
Solution
Write each octal digit as its equivalent bit pattern to get