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Positional value representation systems

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• The Decimal Number System
  • The Best known positional system is decimal number system

  • Value of a digit depends on its position in number:
    • There are 10 digits in use: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

    • The value of a digit increases by 10 for each digit position

    • Hence it is called the decimal (10) number system

  • Example:

    679 6 is in hundreds position (600) 7 is in tens position (70) 9 is in ones position (9) So: 679 ^^^ ||| ||| ||+--- value at 1: 9 x 1 = 9 |+---- value at 10: 7 x 10 = 70 +----- value at 100: 6 x 100 = 600 + -------- represented value = 679

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• The Binary Number System
  • The computer uses the binary number system:

  • Value of a digit also depends on its position in number:
    • There are 2 digits in use: 0, 1

    • The value of a digit increases by 2 for each digit position

    • Hence it is called the binary (2) number system

  • Example 1:

    1011 ^^^^ |||| |||+-- value at 1: 1 x 1 = 1 ||+--- value at 2: 1 x 2 = 2 |+---- value at 4: 0 x 4 = 0 +----- value at 8: 1 x 8 = 8 + -------- represented value = 11 (decimal)

  • Example 2:

    11001 ^^^^^ ||||| ||||+-- value at 1: 1 x 1 = 1 |||+--- value at 2: 0 x 2 = 0 ||+---- value at 4: 0 x 4 = 0 |+----- value at 8: 1 x 8 = 8 +------ value at 16: 1 x 16 = 16 + -------- represented value = 25 (decimal)