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Title: 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
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