Introduction to IT 1, 3 Lecture 3: Data Representation

1
Introduction to IT (1), (3)Lecture 3 Data
Representation
Dr. Haipeng Guo United International College
Fall, 2006
2
Outline

• Distinguish between analog and digital
  information
• Explain data compression and calculate
  compression ratios
• Explain the binary formats for negative values
• Describe the characteristics of the ASCII and
  Unicode character sets
• Explain the nature of sound and its
  representation.
• Explain how RGB values define a color.
• Explain how to represent images graphics.
• Explain how to represent video.

3
Data Representation

• Data comes in many forms
• Numbers 235, 11.01, -24,
• Text hello, world! ??!
• Audio .mp3
• Images and graphics .bmp, gif, JPEG
• Video .avi
• All of the data is stored in computers as binary
  digits
• Data must be represented in a way that
• Captures the essence of the information
• And in a form that is convenient for computer
  processing

4
Data Compression

• Data compression
• Reduction in the amount of space needed to store
  a piece of data.
• Compression ratio
• The size of the compressed data divided by the
  size of the original data.
• A data compression techniques 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.

5
WinRAR

• Currently the best archiver
• WinRAR Tutorial
• http//users.pandora.be/soulmaniacs/winrar.html

6
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 is to represent enough of the world to
  satisfy our computational needs and our senses of
  sight and sound.

7
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 discrete representation,
  breaking the information up into separate
  elements.
• A mercury thermometer is an analog device. The
  mercury rises in a continuous flow in the tube in
  direct proportion to the temperature.

8
Analog Data

• A mercury thermometer is an analog device. The
  mercury rises in a continuous flow in the tube in
  direct proportion to the temperature.

9
Analog and Digital Information

• Computers, cannot work well with analog
  information. So we digitize information by
  breaking it into pieces and representing those
  pieces separately.
• Why do we use binary?
• Modern computers are designed to use and manage
  binary values because the devices that store and
  manage the data are far less expensive and far
  more reliable if they only have to represent on
  of two possible values.

10
Electronic Signals (Contd)

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

11
Analog and Digital Information

• Periodically, a digital signal is reclocked to
  regain its original shape.

An analog and a digital signal
Degradation of analog and digital signals
12
Binary Representation

• One bit can be either 0 or 1. Therefore, one bit
  can represent only two things.
• To represent more than two things, we need
  multiple bits. Two bits can represent four things
  because there are four combinations of 0 and 1
  that can be made from two bits 00, 01, 10,11.

13
Binary Representation
14
Binary Representation

• In general, n bits can represent 2n things
  because there are 2n combinations of 0 and 1 that
  can be made from n bits. Note that every time we
  increase the number of bits by 1, we double the
  number of things we can represent.
• Questions
• How many bits are needed to represent 128 things?
• How many bits are needed to represent 67 things?

15
Representing Negative Values

• You have used the signed-magnitude representation
  of numbers since grade school.
• The sign represents the ordering,
• and the digits represent the magnitude of the
  number.

16
Representing Negative Values

• problem with the sign-magnitude representation.
• There are two representations of zero. There is
  plus zero and minus zero. Two representations of
  zero within a computer can cause unnecessary
  complexity.
• If we allow only a fixed number of values, we can
  represent numbers as just integer values, where
  half of them represent negative numbers.

17
Representing Negative Values

• For example, if the maximum number of decimal
  digits we can represent is two, we can let 1
  through 49 be the positive numbers 1 through 49
  and let 50 through 99 represent the negative
  numbers -50 through -1.
• This representation of negative numbers is called
  the tens complement.

18
Advantages of Using 10s Complement

• To perform addition within this scheme, you just
  add the numbers together and discard any carry.

19
Advantages of Using 10s Complement

• A-BA(-B). We can subtract one number from
  another by adding the negative of the second to
  the first.
• Addition and subtraction become same

20
2s Complement

• 8 bits

• 3 bits
• 000 0
• 001 1
• 010 2
• 011 3
• 100 -4
• 101 -3
• 110 -2
• 111 -1

21
Overflow

• Overflow occurs when the value that we compute
  cannot fit into the number of bits we have
  allocated for the result.
• For example, if each value is stored using eight
  bits, adding 127 to 3 overflows.
• Overflow is a classic example of the type of
  problems we encounter by mapping an infinite
  world onto a finite machine.

22
Overflow
1111111 0000011 10000010
127 3
23
Representing Text

• A text document can be decomposed into chapters,
  paragraphs, sentences, words, and ultimately
  individual characters.
• To represent a text document in digital form, we
  simply need to be able to represent every
  character that may appear.
• In English, a, b, , z, A, B,Z
• The general approach for representing characters
  is to list them all and assign each a binary
  string.
• a ? (01100001)2 ? (97)10 ? 61h

24
Character Set

• A character set is a list of characters and the
  codes used to represent each one.
• By agreeing to use a particular character set,
  computer manufacturers have made the processing
  of text data easier.
• ASCII, Unicode, etc.

25
ASCII

• 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.
• Later ASCII evolved so that all eight bits were
  used which allows for 256 characters

26
ASCII
27
ASCII

• Note that the first 32 characters in the ASCII
  character chart do not have a simple character
  representation that you could print to the
  screen.

28
The Unicode Character Set

• The extended version of the ASCII character set
  is not enough for international use.
• The Unicode character set uses 16 bits per
  character. Therefore, 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.

29
Unicode
30
Representing

• 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.

31
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.

32
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.

33
Representing Audio Information
34
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
• as the disc.
• The laser light reflects strongly
• if the surface is smooth and
• reflects poorly if the surface is pitted.

35
Representing Audio Information

• Audio Formats
• 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 analyzes the frequency spread and
  compares it to mathematical models of human
  psychoacoustics (the study of the interrelation
  between the ear and the brain), then it discards
  information that cant be heard by humans. Then
  the bit stream is compressed to achieve
  additional compression.

36
Representing Color

• Color is our perception of the various
  frequencies of light that reach the retinas of
  our eyes.
• Our retinas have three types of color
  photoreceptor cone cells that respond to
  different sets of frequencies.
• These photoreceptor categories correspond to the
  colors of red, green, and blue.

37
Representing Color

• Color 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 colors.
• For example, an RGB value of (255, 255, 0)
  maximizes the contribution of red and green, and
  minimizes the contribution of blue, which results
  in a bright yellow.

38
Three Dimension Color Space
(0,0,0)
(1,1,1)
39
Representing Images and Graphics

• The amount of data that is used to represent a
  color is called the color depth.
• HiColor is a term that indicates a 16-bit color
  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 color depth.
  Therefore, each number in an RGB value gets eight
  bits.

40
Indexed Color

• A particular application such as a browser
• may support only a certain number of
• specific colors, creating a palette from
• which to choose.
• For example

41
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 a picture
  is called the resolution.
• The storage of image information on a
  pixel-by-pixel basis is called a raster-graphics
  format.
• Several popular raster file formats including
  bitmap (BMP), GIF, and JPEG.

42
BMP
43
Digitized Images and Graphics
High Resolution
44
Digitized Images and Graphics
Low Resolution
45
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.
• The goal is not to lose information that affects
  the viewer's senses.

46
Video Players

• QuickTime Player (Apple)
• Real Player
• VLC media player
• Microsoft Media Player

47
Summary

• Distinguish between analog and digital
  information
• Explain the binary formats for negative values
• Describe the characteristics of the ASCII and
  Unicode character sets
• Explain the nature of sound and its
  representation.
• Explain how RGB values define a color.
• Representing Audio Information
• Representing Images Graphics
• Representing Video Information