Data Representation and Storage

Data Representation and Storage

1. Data Types

   • integer
     • whole number - 7, 0, 15, -5
   • real
     • number with or without a fraction - 7.2, 8.9, -6.8, 12.0
   • character
     • single character - a, @, #, 8, Q
   • string
     • one or more characters - Hello, abc, b, Y
   • boolean
     • true/false

2. Representation of numbers

   • denary/decimal
     • base 10
     • convert to binary
       • 128 64 32 16 8 4 2 1
   • binary
     • 0,1
     • base 2
     • used by computers
   • hex
     • convert to binary
       • 0 = 0000 1 = 0001 2 = 0010 3 = 0011 4 = 0100 5 = 0101 6 = 0110 7 = 0111 8 = 1000 9 = 1001 A = 1010 B = 1011 C = 1100 D = 1101 E = 1110 F = 1111
       • 6F(16) = 01101111(2) = 111(10)
     • 1 2 3 4 5 6 7 8 9 A B C D E F
     • base 16
     • used by people to understand binary better

3. Binary Arithmetic

4. Representation of characters

   • unicode
     • can represent more characters than ASCII but more memory hungry
     • 65000 possible characters
     • uses 16 bits
   • using a standard character set allows data interchange between different programs
   • ASCII
     • 01100001 represents a
     • 256 possible characters
       • 7 bits
     • 01000001 represents A
     • extended ASCII
       • 8 bit
         • 256 characters
   • stored in binary

5. Representation of Graphics

6. Representation of Sound

7. Storage Requirements

8. Compression

   • stores data in a different way that takes up less space in memory and on the hard disk
   • lossless
     • the original data is not altered in any way
       • BBRRRRRYYYRRRRRRRBBBB > 2B, 5R, 3Y, 7R, 4B
         • takes 21 bytes > takes 10 bytes
   • lossy
     • there are small changes made to the original data
       • much more effective but not possible to recreate the original data exactly
       • only useful where slight changes don't matter, such as with images, video or audio
       • any changes to a program would prevent it working and reading text where the letters are different would not be acceptable
   • compression ratio = uncompressed size / compressed size
     • 10MB file, compressed to 2MB would have a compression ratio of 10/2 aka 5 - ratio = 5:1
       • larger numbers mean better compression
   • BMP
     • largest file size - not compressed
   • JPG
     • lossy compression - most effective - smallest in size
   • PNG
     • smaller than uncompressed - not as small as lossy

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