Page 15 - TP_Plus_v4_Class7
P. 15

Let us first learn how to form binary numbers.

                As the binary number system consists of two digits 0 and 1 hence, its base is 2. Each digit or bit in binary
                number system can be either 0 or 1. A combination of binary digits may be used to represent different
                quantities like 1001. The positional value of each digit in binary number is twice the place value or face
                value of the digit to its right. The weight of each position is a power of 2.

                The place value of the digits according to position and weight is as follows:
                            Position        3         2         1         0                   –1        –2
                                                                                     •
                             Weights       2 3       2 2        2 1       2 0                 2 –1      2 –2



                          Factbot

                  A single binary digit (like '0' or ‘1’) is called a ‘bit’. For example 11010 is five bits long. The word bit is made up
                  of the words 'binary digit’.


                Octal Number System
                                                                                  Position        7       6       5
                The octal number system consists of eight digits from 0 to 7.     Weight          8 2     8 1     8 0
                Hence, the base of octal number system is 8. In this system, the                       2       1       0
                position of each digit represents a power of 8. Any digit in this   Real Value of  7 × 8  6 × 8   5 × 8
                system is always less than 8. Octal number system is used as a    each digit
                shorthand representation of long binary numbers. The number (841)  is not valid in this number system as
                                                                                    8
                8 is not a valid digit. The place value of digits according to the position and weight are given in table.

                Hexadecimal Number System

                The hexadecimal number system consists of 16 digits from 0 to 9 and letters from A to F. The letters A to
                F represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position
                in hexadecimal number system represents a power of 16. For example, the number (764)  is a valid
                                                                                                             16
                hexadecimal number. It is different from (764)  which is seven hundred and sixty four. This number
                                                                10
                system provides shortcut method to represent long binary numbers. Representation of Hexadecimal
                Number System into Decimal Form.

                  Hexadecimal       0    1    2     3    4     5    6     7    8     9    A    B     C    D     E    F
                     Decimal        0    1    2     3    4     5    6     7    8     9   10    11   12    13   14    15


                     DECIMAL TO BINARY CONVERSION

                To convert a decimal number into a binary number, follow these steps:

                    Divide the decimal number by 2 (the base of the binary number system).
                    Note down the quotient and the remainder.
                    Divide the quotient obtained again by 2 and note down the resulting quotient and remainder.

                    Repeat the procedure till you reach a quotient less than 2.
                     Firstly, list the last quotient and all the remainders (moving from bottom to top). You will get your
                   binary number.


                                                                                                   #Number System  13
   10   11   12   13   14   15   16   17   18   19   20