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Example 2: Convert (4AB.2)  to binary.
                                       16
              Answer:

                  4      10(A)    11(B)     .        2
                 0100    1010     1011      .      0010
              Binary equivalent is (0100 1010 1011.0010) 2

              After removing leading 0s in the integer part and trailing 0s in the fractional part
              = (10010101011.001)
                                 2

              1.2.11 Octal to Hexadecimal and Hexadecimal to Octal
              The steps to be followed are:
              1.  To convert octal to hexadecimal, first convert octal to binary and binary to hexadecimal by the steps mentioned
                 above.
 8 (2 )  4 (2 )  2 (2 )  1 (2 )  Hexa
 3
 0
 1
 2
              2.  Similarly, to convert hexadecimal to octal, convert hexadecimal to binary and the binary to octal as shown
 0  1  0  1  0 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 5  above.
 0  1  0  0  0 × 8 + 1 × 4 + 0 × 2 + 0 × 1 = 4
 1  1  1  1  1 × 8 + 1 × 4 + 1 × 2 + 1 × 1 = 15  Note: The above conversion can be done by first converting number of one base to decimal and then the
                     decimal number to number of another base. Previous mentioned method has been followed in this book
                     as it makes calculation simpler.

              Example 1: Convert (2517)  to hexadecimal.
                                      8
                                                                            1
                                                                  2
                                                                                      0
              Answer: Converting Octal to Binary first         4 (2 )    2 (2 )    1 (2 )             Octal
                   2          5          1         7             0         1         0         0 × 4 + 1 × 2 + 0 × 1 = 2
                  010        101        001       111            1         0         1         1 × 4 + 0 × 2 + 1 × 1 = 5
                                                                 0         0         1         0 × 4 + 0 × 2 + 1 × 1 = 1
              Binary equivalent is (010101001111)                1         1         1         1 × 4 + 1 × 2 + 1 × 1 = 7
                                               2
              Converting Binary to Hexadecimal after Grouping 0101 0100  1111.

                                                                                        0
                                                                         2
                                                                 3
                                                                                1
                   0101           0100          1111          8 (2 )  4 (2 )  2 (2 )  1 (2 )          Hexa
                     5             4            15(F)           0      1       0      1     0 x 8 + 1 x 4 + 0 x 2 + 1 x 1 = 5
                                                                0      1       0      0     0 x 8 + 1 x 4 + 0 x 2 + 0 x 1 = 4
                                                                1      1       1      1     1 x 8 + 1 x 4 + 1 x 2 + 1 x 1 =15
              (54F) 16
              Example 2: Convert (621.04)  to hexadecimal.
                                        8
              Answer: Converting Octal to Binary first
                                                                  2
                                                                            1
                                                                                      0
                 6       2      1      .      0       4        4 (2 )    2 (2 )    1 (2 )             Octal
                110     010    001     .     000     100         1         1         0         1 × 4 + 1 × 2 + 0 × 1 = 6
              Binary equivalent is (110 010001.000100) 2         0         1         0         0 × 4 + 1 × 2 + 0 × 1 = 2
              Grouping 4 bits                                    0         0         1         0 × 4 + 0 × 2 + 1 × 1 = 1
              Converting Binary to Hexadecimal after ignoring    0         0         0         0 × 4 + 0 × 2 + 0 × 1 = 0
              trailing 0s in fractional part and adding 3 0s     1         0         0         1 × 4 + 0 × 2 + 0 × 1 = 4
              before 1







                2424  Touchpad Computer Science-XI
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