NUMBER SYSTEMS  

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LEARNING OBJECTIVES
In this chapter yo u will learn about :

  • Non-potensitional number system
  • Positional number system
  • Decimal number system 
  • Binary number system
  • Octal number system
  • Hexadesimal number system

A. NUMBER SYSTEM
     Two types of number system are : 

      1. Non-positional number system
  •  Characteristics : Each symbol represents the same value regardless of its position in the number, the symbols are simply added to find out the value of a particular number
  • Difficulty : it is difficult to perform aritmmatic with such a  number  system
      2. Positional number system 
  • Use only a few symbol called digits
  • These symbols represent different value depending on the pasition they occupy in the number
  • The maximum value of a single digit is always equal to one less than the value of the base

     
3. Decimal number system

  • Characteristics : A positional number system. The maximum value of a single digit is 9 (one less than the value of the base). Each position of a digit represents a spesific power of the base (10). We use this number system in our day-to-day life.


      4. Binary number system

  • Characteristics : A positional number system. Has only 2 symbols or digit (0 and 1). Hence its base = 2. The maximum value of a single digit is 1 (one less than the value of the base). Each position of a digit represents a specific power of the base (2). This number system is used in computers.

     
5. Octal number system
  • Characteristics : A positional number system. Has total 8 symbols or digits (0, 1, 2, 3, 4, 5, 6, 7), Hence, its base = 8. the maximum value of a single digit is 7 (one less than the value of the base). Each position of a digit represents a spesific power of the base (8). Since there are only 8 digits, 3 bits are sufficient to represent any octal number in binary.



      6. Hexadecimal number system

  • Characteristics : A positional number system. Has total 16 symbol or digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F), Hence its base = 16. The symbols A, B, C,D, E and F represent the decimal value 10, 11, 12, 13, 14 and 15 respectively. The maximum value of a single digit is 15 (one less than the value of the base). Each position of a digit represents a specific power of the base (16). Since there are only 16 digits, 4 bits are sufficient to represent any hexadecimal number in binary.

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