Number system and their conversions

NUMBER SYSTEM

  • A mathematical notation for representing numbers is known as number system.
  • number system  is a  system for expressing numbers .
  • Collection of digits forms a number, which can be divided in two parts : Integer and fractional part that set apart by a radix point  , shown below

Also,                     

for example: In decimal number system,
base is 10 ,So digit in integer or fractional part is equal to ( 0 or 10-1 )  or in between ( 0 to 10-1 )
i.e. ( 0 1 2  3 4  5 6 7 8 9 ).

  • Now, Each digit assigned some weight in positional number system.The digit in the number are placed side by side and each position in the number is assigned a weight by some defined rules.
  • In any number system, there is a set of symbols with rules defined for performing arithmetic operations .
  • The same sequence of symbols may represent different numbers in different number systems. For example, “10 represents the number “two” in the binary number system and the number “ten” in the decimal number system .
  • What is base or radix ?
    The radix or base is the number of unique digits,  used to represent numbers in a any number system. For example, In decimal number system the radix is ten, since it using ten digits from 0 through 9.
    Similarly, In binary number system, radix or base is 2, since it is having two digits 0 and 1.Some commonly used number system:
  • Decimal number system
    base /radix = 10
    symbol used=0 1 2 3 4 5 6 7 8 9
    weight assigned to position  =10i  in integer part and 10-f   in fractional part
    for example:
    (425.63)10
     
  • Binary number system
    base /radix = 2
    symbol used=0 1
    weight assigned to position  =2i  in integer part and 2-f   in fractional part
    for example:
    (101.10)2

  • Octal number system
    base /radix = 8
    symbol used=0 1 2 3 4 5 6 7
    weight assigned to position  =8i  in integer part and 8-f   in fractional part
    for example:
    (672.13)8

  • Hexadecimal number system
    base /radix = 16
    symbol used=0 1 2 3 4 5  6 7 8 9 A B C D E  F
    here (A=10,B=11,C=12,D=13,E=14,F=15)
    weight assigned to position  =16i  in integer part and 16-f   in fractional part
    for example:
    (A23.1F)16


    Binary number system
    Binary to decimal conversion
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