Chapter 3, Data Representation

Goals

• distinguish between digital and analog information
• explain data compression and calculate compression ratios
• explain binary formats for negative and floating-point numbers
• describe the characteristics of the ASCII and Unicode character sets
• perform various types of text compression
• explain the nature of sound and its representation
• explain how RGB values define a color
• distinguish between raster and vector graphics
• explain temporal and spatial video compression

Data and Computers

• Computers, without data, are useless
• We need efficient ways to represent and organize this data
• Types of data
  • Numbers, letters (text)
  • Sound (audio)
  • Images, still and moving (graphics, video)
• MULTIMEDIA - several different media types
  • Probably referring to text, sound and graphics
  • Possibly CD rom (or DVD)
• Data Compression - Reducing the amount of space needed to store a piece of data
  • Save disk space
  • Not a problem with text files, but audio and video becomes a problem
  • Personal MP3 Players.
    • Download data
    • Sizes 64K to 40 GB
    • Size of device plus compression determine how much music you can store.
  • Compression Ratio - size after compression divided by size before compression
    • If a file was originally 200K and compressed to 100K the compression ratio is 100/200 = .5
    • If a file was originally 200K and compressed to 40K the compression ration is 40/200 = 2/10 = .2
  • If a compression technique preserves all of the information, the the compression technique is called lossless, or if data is lost it is known as lossy
    • Lossless compression is preferred.
    • But sometimes, we can save quite a bit of space using a lossy compression technique
    • but only when the loss of data doesn't hurt.
      • The following images are from the WebMuseum, Paris
      • Some different quality
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        You have a tradeoff of space (or quality) for size
        In every part of data storage/transmission
        Analog vs Digital

        • Stored as a position - analog
        • Stored as a number digital
        • Continuous vs Discrete
        • From www.rolex.com
        • From www.kmart.com
        • Whis is better?
        • Digitize convert into digital data.
        Why Binary?

        • Easier to detect on/off
        • Electronic signal stabalization
        Bits requried for representation

        • 1 bit, 0 or 1 two things (2¹)
        • two bits (00, 01, 10, 11) four things, (2²)
        • three bits (000, 001, 010, 011, 100, 101, 110, 111) eight things, (2³)
        On the other hand, how many bits do we need to represent n things?

        • 5? (more than 4 less than 8) 3 bits
        • 12? (more than 8 less than 16) 4 bits
        • ceiling - integer greater than or equal to
        • ceil(4) = 4
        • ceil(4.2) = 5
        • ceil(4.99) = 5
        • lg is the log base two of a number
        • if a = 2^x then lg(a ) = x
        • lg(8) = 3
        • lg(16) = 4
        • lg(10 ) = 3.32.
        • You need ceil(lg(n)) bits to represent n things.
        • Easy/Hard method, find next larger power of two
        • Hard/Easy method ceil(lg(n))
        • Why do we care?

        Image	Size	Compression Ratio
        Original	346K
        95	190K	.55
        75	85K	.25
        50	50K	.14
        25	26K	.075
        10	12K	.035