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    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

                           Octal Number System

                      The octal number system consists of eight digits from 0 to 7. Hence, the base of octal number system
                      is 8. In this system, the position of each digit represents a power of 8. Any digit in this system is always
                      less than 8. Octal number system is used as a shorthand representation of long binary numbers. The
                      number (841)  is not valid in this number system as 8 is not a valid digit.
                                   8
                           Hexadecimal Number System

                      The hexadecimal number system consists of 16 digits from 0 to 9 and 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 hexadecimal
                                                                                                 16
                      number. It is different from (764)  which is seven hundred and sixty four. This number system provides
                                                      10
                      shortcut method to represent long binary numbers.

                             DECIMAL TO BINARY CONVERSION

                      To convert a decimal number into a binary number, follow these steps:
                      Step 1:   Divide the decimal number by 2 (the base of the binary number system).
                      Step 2:  Note down the quotient and the remainder.
                      Step 3:  Divide the quotient obtained again by 2 and note down the resulting quotient and remainder.
                      Step 4:  Repeat the procedure till you reach a quotient less than 2.
                      Step 5:   List the last quotient and all the remainders (moving from bottom to top). You will get your
                              binary number.

                      Look at the given examples to understand the conversion better.

                      Example 1: Convert the decimal number 26, i.e., (26)  to binary.
                                                                           10
                                        2  26
                                        2   13    0      The binary equivalent of (26)  is 11010
                                                                                      10
                                        2    6    1      In other words, (26)  = (11010) 2
                                                                             10
                                        2    3     0
                                             1     1

                                                         Start listing the last quotient and all the
                                                         remainders from here.

                      10    Premium Edition-VII

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