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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.






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