Page 10 - TP-Play_V-2.0_Book-8
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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 number. It is different from (764)  which is seven hundred and
                 16                                                             10
            sixty four. This number system provides 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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