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Page 16 - 2505_CoreGPT(Podar)_Flipbook_C7
P. 16

    = 192 + 8 + 4

                                    = 204
                      Therefore, (314)  = (204)
                                       8        10
                      Hexadecimal to Decimal Number System

                      To convert a hexadecimal number to a decimal number, follow these steps:
                      Step 1  Multiply each digit (or  alphabet  value) of the given hexadecimal number by the

                               corresponding power of 16, starting from the rightmost digit.
                      Step 2  The exponents of 16 should start with 0 for the rightmost digit and increase by 1 as you

                               move left.
                      Step 3  Simplify each product and add them together to get the decimal equivalent.

                      The given examples will help you understand the conversion.
                      Example 1:  Convert (125)  to a decimal number.
                                                   16
                                             2
                                                       1
                                    = 1 × 16  +2 × 16  + 5 × 16   0
                                    = 1 × 256 + 2 × 16 + 5 × 1
                                    = 256 + 32 + 5

                                    = 293
                      Therefore, (125)  = (293)
                                       16        10
                      Example 2:  Convert (5AD)  to a decimal number.
                                                   16
                                        A = 10 (since A represents 10 in hexadecimal)

                                        D = 13 (since D represents 13 in hexadecimal)
                                                    2
                                                                1
                                          = 5 × 16  + 10 × 16  + 13 × 16    0
                                          = 5 × 256 + 10 × 16 + 13 × 1
                                          = 1280 + 160 + 13

                                          = 1453
                      Therefore, (5AD)  = (1453)
                                       16          10

                             Restart

                             A number system is method of counting.
                             The decimal number system consists of ten digits from 0 to 9.
                            The binary number system consists of two digits 0s and 1s.
                             The octal number system consists of eight digits from 0 to 7.
                             The hexadecimal number system consists of 16 digits from 0 to 9 and A to F.

                     14     Premium Edition-VII

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