Page 12 - Chinmaya_C7_flipbook
P. 12

OCTAL NUMBER SYSTEM
                  A number system made up of eight digits from 0 to 7, is known as the octal number system.
                  When the octal number system is used, every number is formed using 0, 1, 2, 3, 4, 5, 6 and 7.
                  The base of the octal number system is 8. It is also known as the base-8 system. Each positioning
                  number represents the power of base 8.

                  For example: (1763) 8
                                  2
                         3
                                            1
                  = (1 x 8 ) + (7 x 8 ) + (6 x 8 ) + (3 x 8 )
                                                      0
                  = (1 x 512) + (7 x 64) + (6 x 8) + (3 x 1)
                  = 512 + 448 + 48 + 3
                  = 1011 or (1011) 10


                  HEXADECIMAL NUMBER SYSTEM
                  A number system made up of sixteen symbols, 0 to 9, and A to F is known as the hexadecimal
                  number system. When the hexadecimal number system is used, every number is formed using
                  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F, where A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15.
                  The base of the hexadecimal number system is 16. It is also known as the base-16 system. Each
                  position represents a power of base 16.
                  For Example: (2AF)  16

                          2
                                     1
                  = (2 x 16 ) + (A x 16 ) + (F x 16 )
                                               0
                  = (2 x 256) + (10 x 16) + (15 x 1)
                  = 512 + 160 + 15

                  = (687) 10
                  The hexadecimal  number  system  has  made  the  representation  of  large  values  easy.  The
                  hexadecimal numbers are used to represent colours on a webpage, that's why programmers
                  now prefer hexadecimal numbers. Some examples of colour code are:

                      Red: #FF0000          Green: #00FF00          Blue: #0000FF




                       Tick ( ) if you know this.
                       ▶   A hexadecimal number system is made up of sixteen symbols, 0 to 9, and A to F.

                       ▶  Number system is a method of counting and representing numbers.




                            CONVERSION OF DECIMAL TO BINARY

                  To convert a decimal number into a binary number, follow the given steps:

                  Step  1    Divide the number to be converted by 2 while keeping track of the quotient and remainder.

                  Step  2    Continue dividing the quotient by 2 until you get a quotient of 0.




                   10   Premium Edition-VII
   7   8   9   10   11   12   13   14   15   16   17