1. Chapter 3 Data Representation

2. Data and Computers
Computers are multimedia devices, dealing with many categories of information. Computers store, present, and help modify:
Numbers
Text
Audio
Images and graphics
Video

3. Analog and Digital Information
Computers are finite. Computer memory and other hardware devices have only so much room to store and manipulate a certain amount of data. The goal of data representation is to represent enough of the world to satisfy our computational needs and our senses of sight and sound.

4. Analog and Digital Information
Information can be represented in one of two ways: analog or digital.
Analog data: A continuous representation, analogous to the actual information it represents.
Digital data: A series of discrete representations, breaking the information up into separate elements.

5. Analog and Digital Information
A mercury thermometer exemplifies analog data as it continually rises and falls in direct proportion to the temperature.
Digital displays only show discrete information.

6. Analog and Digital Information
Computers cannot work well with analog information, so we digitize it by sampling it at discrete intervals and representing each interval by a numeric value.

7. Electronic Signals
An analog signal continually fluctuates up and down in voltage. But a digital signal has only a high or low state, corresponding to the two binary digits.
An analog and a digital signal

8. Electronic Signals
All electronic signals (both analog and digital) degrade as they move down a line. That is, the voltage of the signal fluctuates due to environmental effects.
Degradation of analog and digital signals

9. Electronic Signals (Cont’d)
Even when it has deteriorated, it is possible to distinguish the 2 states of a digital signal by comparison to the threshold.
Periodically, a digital signal can be reclocked to regain its original shape.
No such process is available for analog signals.

10. Representing Text

11. Representing Text
To represent a text document in digital form, we need to be able to represent every possible character that may appear.
There is a finite number of characters to represent, so the general approach is to list them all and assign each a binary string.

12. Representing Text
A character set is a list of characters and the codes used to represent each one.
In 1960, a survey revealed 60 different characters sets in use.
At IBM alone there were 9 different sets.
By agreeing to use ONE particular character set, computer manufacturers have made the processing of text data easier.

13. The ASCII Character Set
ASCII stands for American Standard Code for Information Interchange.
The ASCII character set originally used seven bits to represent each character, allowing for 128 unique characters.
Wikipedia has an excellent entry on ASCII.

14. The ASCII Character Set (7 bit)

15. The ASCII Character Set
Notice the organisation of the ASCII table.
The table divides in half according to the MSB.
Letters are all in the second half so all codes for alphabetic characters start with 1.
This second half of the table divides in half again according to the next bit:
UPPERCASE letters start 10.
lowercase letters start 11.
The first half of the table also divides in half according to the next bit:
Control characters start 00.
Numerals and punctuation start 01.

16. The ASCII Character Set
Note that control characters (the first 32 in the ASCII character set) do not have simple character representations that you could print to the screen.
Many, however, perform actions with which you are familiar.
Some have there own keys, others need to be constructed.

17. The ASCII Character Set Control Characters
Control sequences are created by holding the Ctrl key (control) and pressing a letter.
This has the effect of subtracting 64 from the ASCII value of the letter pressed.
For example:
‘M’ has ASCII value 77 ( in binary),
Ctrl-M has ASCII value 13 ( in binary).
Alternately, we can see this as “masking bit 6.”

18. The ASCII Character Set Common Control Characters
Hex
Binary
Decimal
Name
Function 00
NUL
Null 07 7
BEL
Bell 08 8 BS
Backspace 09 9 HT
Horizontal Tab 0A 10 LF
Line Feed 0B 11 VT
Vertical Tab 0C 12 FF
Form Feed 0D 13 CR
Carriage Return 0E 14 SO
Shift Out 0F 15 SI
Shift In 1B 29
ESC
Escape

19. The ASCII Character Set
Coding letters in ASCII is easy.
Let’s look at ‘j’ as an example:
Since ‘j’ is a letter, its code starts with a 1.
Since it’s lowercase, the next bit is also a 1.
Since it’s the tenth letter of the alphabet the rest of the code is
The complete ASCII code for ‘j’ is

20. The ASCII Character Set
ASCII evolved so that eight bits are used.
The 7-bit codes were simply prefixed with another bit, giving another natural doubling.
The original 7-bit codes were padded with 0.
So the code for ‘j’ became
128 new characters were added. The codes for this alternate character set start with 1.

21. The Unicode Character Set
Even the extended version of the ASCII character set is not enough for international use.
The Unicode character set uses 16 bits per character. The Unicode character set can represent 216, or over 65 thousand characters.
Unicode was designed to be a superset of ASCII. That is, the first 256 characters in the Unicode character set correspond exactly to the extended ASCII character set.

22. Examples of Unicode Characters
Figure 3.6 A few characters in the Unicode character set

23. Compressing Files

24. Data Compression
It is important that we find ways to store and transmit data efficiently, which leads computer scientists to find ways to compress it.
Data compression is a reduction in the amount of space needed to store a piece of data.
Compression ratio is the size of the compressed data divided by the size of the original data.

25. Data Compression A data compression technique can be
lossless, which means the data can be retrieved without any loss of the original information,
lossy, which means some information may be lost in the process of compaction.
As examples, consider these 3 techniques:
keyword encoding
run-length encoding
Huffman encoding

26. Keyword Encoding
Frequently used words are replaced with a single character. For example…
Note, that the characters used to encode cannot be part of the original text.

27. Keyword Encoding Consider the following paragraph,
The human body is composed of many independent systems, such as the circulatory system, the respiratory system, and the reproductive system. Not only must all systems work independently, they must interact and cooperate as well. Overall health is a function of the well-being of separate systems, as well as how these separate systems work in concert.

28. Keyword Encoding
This version highlights the words that can be replaced.
The human body is composed of many independent systems, such as the circulatory system, the respiratory system, and the reproductive system. Not only must each system work independently, they must interact and cooperate as well. Overall health is a function of the well-being of separate systems, as well as how those separate systems work in concert.

29. Keyword Encoding This is the encoded paragraph:
The human body is composed of many independent systems, such ^ ~ circulatory system, ~ respiratory system, + ~ reproductive system. Not only & each system work independently, they & interact + cooperate ^ %. Overall health is a function of ~ %- being of separate systems, ^ % ^ how # separate systems work in concert.

30. Keyword Encoding
There are a total of 349 characters in the original paragraph including spaces and punctuation.
The encoded paragraph contains 314 characters, resulting in a savings of 35 characters.
The compression ratio for this example is 314/349 or approximately 0.9.

31. Keyword Encoding
A compression ratio of .9 (90%) is NOT very good. The compressed file is 90% the size of the original.
However, there are several ways this can be improved. Can you think of some?

32. Run-Length Encoding
A single character may be repeated over and over again in a long sequence. This type of repetition doesn’t generally take place in English text, but often occurs in large data streams.
In run-length encoding, a sequence of repeated characters is replaced by:
a flag character,
followed by the repeated character,
followed by a single digit that indicates how many times the character is repeated.

33. Run-Length Encoding Some examples: AAAAAAA would be encoded as *A7
*n5*x9ccc*h6 some other text *k8eee can be decoded into the following original text:
nnnnnxxxxxxxxxccchhhhhh some other text kkkkkkkkeee

34. Run-Length Encoding
In the second example, the original text contains 51 characters, and the encoded string contains 35 characters, giving us a compression ratio of 35/51 or approximately 0.68.
Since we are using one character for the repetition count, it seems that we can’t encode repetition lengths greater than nine. However, instead of interpreting the count character as an ASCII digit, we could interpret it as a binary number.

35. Huffman Encoding
Why should the blank, which is used very frequently, take up the same number of bits as the character “X”, which is seldom used in text?
Huffman codes use variable-length bit strings to represent each character.
A few characters may be represented by five bits, and another few by six bits, and yet another few by seven bits, and so forth.

36. Huffman Encoding
If we use only a few bits to represent characters that appear often and reserve longer bit strings for characters that don’t appear often, the overall size of the document being represented will be smaller.

37. Huffman Encoding
An example of a Huffman alphabet

38. Huffman Encoding
DOORBELL would be encoded in binary as
If we used a fixed-size bit string to represent each character (say, 8 bits), then the binary from of the original string would be 64 bits.
The Huffman encoding for that string is 25 bits long, giving a compression ratio of 25/64, or approximately 0.39.
An important characteristic of any Huffman encoding is that no bit string used to represent a character is the prefix of any other bit string used to represent a character.

39. Representing Audio Data

40. Representing Audio Information
We perceive sound when a series of air compressions vibrate a membrane in our ear, which sends signals to our brain.
A stereo sends an electrical signal to a speaker to produce sound. This signal is an analog representation of the sound wave. The voltage in the signal varies in direct proportion to the sound wave.

41. Representing Audio Information
To digitize the signal we periodically measure the voltage of the signal and record the appropriate numeric value. The process is called sampling.
In general, a sampling rate of around 40,000 times per second is enough to create a reasonable sound reproduction.
The standard sampling rate for CDs is 44.1 kHz. The Pro Audio standard is 48 kHz.

42. Representing Audio Information
Figure 3.8 Sampling an audio signal

43. Representing Audio Information
It should be noted that the potential loss of peak values suggested in the previous slide is a myth. The time lapse between samples is much too short for any such loss.
The human ear hears sounds between 20 Hz and 20,000 Hz. Sampling at twice this frequency (44,000+) eliminates any potential loss of data.
For a complete explanation refer to the Nyquist–Shannon sampling theorem.

44. Representing Audio Information
A compact disk (CD) stores audio information digitally. On the surface of the CD are microscopic pits that represent binary digits. A low intensity laser is pointed at the disc. The laser light reflects strongly if the surface is smooth and reflects poorly if the surface is pitted.

45. Representing Audio Information
Figure A CD player reading binary information

46. Audio Formats Audio Formats MP3 is dominant
WAV, AU, AIFF, VQF, and MP3.
MP3 is dominant
MP3 is short for MPEG-2, audio layer 3 file.
MP3 employs both lossy and lossless compression.
First it analyses the frequency spread and compares it to mathematical models of human psychoacoustics (the study of the interrelation between the ear and the brain), and it discards information that can’t be heard by humans.
Then the bit stream is compressed using a form of Huffman encoding to achieve additional compression.

47. Representing Graphic Images

48. Representing Images and Graphics
Colour is our perception of the various frequencies of light that reach the retinas of our eyes.
Our retinas have three types of colour photoreceptor cones which respond to different sets of frequencies. These photoreceptor categories correspond to the colours of red, green, and blue.

49. Representing Images and Graphics
Colour is often expressed in a computer as an RGB (red, green, blue) value, which is actually three numbers that indicate the relative contribution of each of these three primary colours.
For example, an RGB value of (255, 255, 0) maximizes the contribution of red and green, and minimizes the contribution of blue. The resulting colour is a bright yellow.

50. Representing Images and Graphics
Figure Three-dimensional color space

51. Representing Images and Graphics

52. Representing Images and Graphics
The amount of data that is used to represent a colour is called the colour depth.
HiColor is a term that indicates a 16-bit colour depth. Five bits are used for each number in an RGB value and the extra bit is sometimes used to represent transparency.
TrueColor indicates a 24-bit colour depth. Therefore, each number in an RGB value gets eight bits.

53. Representing Images and Graphics
HiColor uses 5 bits for each number.
Since 25 = 32, there are 32 different levels for each of the 3 primary colours. So there are 323 (or 215) possible colours.
This is a total of 32,768 different colours.
TrueColor uses eight bits for each colour component.
28* 28* 28 = 224 or 16,777,216 colours.
Some monitors can use as many as 32 bits for colour depth.
This is potentially 4,294,967,296 colours!

54. Representing Images and Graphics
The human eye is able to distinguish about 200 intensity levels in each of the three primaries red, green, and blue. All in all, up to 10 million different colours can be distinguished.
So modern monitors are examples of solutions without a problem.
If the human eye can distinguish only 10 million colours, why develop monitors that can display over 4 billion?

55. Indexed Colour
A particular application such as a browser may support only a certain number of specific colours, creating a palette from which to choose. For example, Netscape Navigator’s colour palette has only 216 colours.

56. Digitized Images and Graphics
Digitizing a picture is the act of representing it as a collection of individual dots, called pixels.
The number of pixels used to represent an image is called the resolution.
As an example, the resolution of many monitors is 1024 X 768, or 786,432 pixels.
If the colour of each pixel is stored as 24 bits (3 bytes) of data, the screen alone requires 2,359,296 bytes (2 megabytes) of memory.

57. Digitized Images and Graphics
Figure A digitized picture composed of few individual pixels

58. Digitized Images and Graphics
Figure A digitized picture composed of many individual pixels

59. Digitized Images and Graphics
The storage of image information on a pixel-by-pixel basis is called a raster-graphics format.
There are several popular raster file formats including:
BMP (bitmap)
GIF (Graphics Interchange Format)
JPEG (Joint Photographic Experts Group)

60. Vector Graphics
Instead of assigning colours to pixels as we do in raster graphics, a vector-graphics format describes an image in terms of lines and geometric shapes.
A vector graphic is a series of commands that describe a line’s direction, thickness, and colour. The file size for these formats tends to be small because every pixel does not need to be represented.

61. Vector Graphics
Vector graphics can be resized mathematically, and these changes can be calculated dynamically as needed.
This makes them particularly useful for defining scalable fonts.
However, vector graphics is not a good technique for representing real-world images.

62. Representing Video Data

63. Representing Video
A video codec (COmpressor/DECompressor) refers to the methods used to shrink the size of a movie to allow it to be played on a computer or over a network.
Almost all video codecs use lossy compression to minimize the huge amounts of data associated with video.

64. Representing Video
To simulate motion, movies need to record (and play back) at least 12 frames per second.
However, good sound quality requires 24 frames/s.
24 frames/s = 1440 frames/minute = frames/hour

65. Representing Video *This is a very conservative resolution. Recall…
If each frame has a resolution of 1024 x 768* there are 786,432 pixels in a frame.
If the colour of each pixel is stored as 24 bits (3 bytes) of data, one frame alone requires 2,359,296 bytes (2 MB) of memory.
An hour of film then, requires 203,843,174,400 bytes (194,400 MB – more than 190 Gigabytes) of storage – just for the images.
*This is a very conservative resolution.

66. Representing Video
The first step in compressing video is to reduce the amount of information stored for a frame.
This problem is essentially the same as that faced when compressing still images.
Spatial compression: A technique based on removing redundant information within a frame.

67. Representing Video Each compressed frame will still be quite large.
Moreover, each one is a still picture that looks very much like the one before it. After all, how much can change in 1/24 of a second?
Why should we waste space to duplicate all of the identical information?

68. Representing Video
We can save even more space by recognizing that between two frames, most of the image hasn’t changed. Storing only the changes (deltas) from one cell to the next is much more efficient.
Temporal compression A technique based on storing differences between consecutive frames.