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Number System

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We are familiar with numbers, characters and symbols. But this type of data are not suitable for microprocessor, logic circuits, computers etc. For this reason data is converted into electronic pulses and each pulse is identified as code. Then this code is converted into numeric format by ASCII, where each number, character and symbol have numerical equivalent. E.g.: Character A has ASCII value 65.

Using this equivalent, the data is interchanged into numeric format. For this numeric conversions we use number systems having a base number, which indicates the number of digits in that number system.

Types of number system

Binary Number System

  • Represents two types of digits 0's and 1's, so the base of number system is 2.
  • Uses two types of electronic pulses, where absence of pulse shows 0 and presence of pulse shows 1.
  • Each binary digit is called as bit.
  • Left-most bit of a number is known as Most Significant Bit (MSB) and right-most bit is known as Least Significant Bit (LSB). Its same for all number system.
  • A group of 4 bit is called as nibble and group of 8 bit is called as byte.
  • Value of digit is determined by the position of digit in the number, where lowest value is for the right-most position and each successive position to the left has a higher place value. Its same for all number system.
  • Examples: a) (010101)2 b) (1010.101)2

Octal Number System

  • Represents 8 types of digits from 0 to 7, so the base of number system is 8.
  • It takes exactly three binary digits to represent an octal digit.
  • Binary 000 is same as octal digit 0, binary 001 is same as octal 1, and so on.
  • Insufficient to convert values into bytes(8 bit), so not widely used in computers.
  • Examples: a) (03105)8 b) (4237.23)8

Decimal Number System

  • Represents 10 types of digits from 0 to 9, so the base of number system is 10.
  • This is the most familiar number system with everyone.
  • Examples a) (582938)10 b) (3797.902)10

Hexadecimal Number System

  • Represents 16 types of digits from 0 to 9 and alphabets from A to F, so the base of number system is 16.
  • Digits from 10 to 15 are represented as 10-A, 11-B, 12-C, 13-D, 14-E, 15-F.
  • As numeric digits and alphabets are used to represent digits, this number system is also called as alphanumeric number system.
  • More complex number system and widely used in computer system.
  • Examples: a) (AF38)16 b) (CE7.5B)16

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Tip Box

Two great indian mathematicians, Aryabhata of Kusumapura developed the place-value notation in the 5th century and a century later Brahmagupta introduced the symbol for zero.


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