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Table 2.5: Decimal and Binary equivalent of Octal Digits.

                                                       Decimal       Binary representation
                                    Octal digit
                                                    representation         (3 bits)
                                        0                 0                  000
                                        1                 1                  001
                                        2                 2                  010
                                        3                 3                  011
                                        4                 4                  100
                                        5                 5                  101
                                        6                 6                  110
                                        7                 7                  111

        The octal number system is also a positional number system. Therefore, each octal digit in an octal number is expressed
        as the sum of products of its digits' place values and their face values symbol value. For fractional numbers, the values
        of digits on the left side of the radix point (octal point) are expressed as positive powers of eight, while values of digits
        on the right side of the radix point are represented as negative powers of eight.
        Table 2.6 shows the digit's place value, face value, and value represented by an octal number (307.24) .
                                                                                                   8
                               Table 2.6: Digit's place value, face value, value represented by (307.24) .
                                                                                        8
                                                                                        1
                                                  1
                                                              0
                                     2
                Digit's place value  8  (=64)    8  (=8)     8  (=1)              8  (=  )     8  (=   1  )
                                                                                                -2
                                                                                   -1
                                                                                        8           64
                Octal digit            3            0          7           .          2           4
                Face value             3            0          7           .          2           4
                Value  represented   3 × 8 2      0 × 8 1    7 × 8 0               2 × 8 -1     4 × 8 -2
                by digit

        The decimal value of (307.24) can be calculated as follows:
                                   8
            (307.24)
                   8
                                      -1
            =3 × 8 + 0 × 8 + 7 × 8 + 2 × 8  + 4 × 8 -2
                 2
                        1
                               0
            =3 × 64 + 0 × 8 + 7 × 1 + 0.25 + 0.0625
            =192 + 7 + 0.25 + 0.0625
            =199.3125

        2.4 Hexadecimal Number System (Base-16)

        The hexadecimal number system (also called the base 16 number system) comprises sixteen distinct digits: 0, 1, 2, 3, 4,
        5, 6. 8, 9, A, B, C, D, E, and F. While digits 0, 1, 2, 3, 4, 5, 6. 8, and 9 in the hexadecimal system have the same meaning
        as the respective digits in the decimal system, the symbols A, B, C, D, E, and F denote the numbers ten, eleven, twelve,
        thirteen, fourteen, and fifteen, respectively. Hexadecimal numbers and digits are also called hex numbers and hex
        digits, respectively. The hexadecimal number system is also a positional number system. Examples of hexadecimal
        numbers are (AB8.6F) , (DAF) , and (D9F.B6C) . Like the octal number system, the hexadecimal number system also
                                   16
                            16
                                                  16
        provides a compact representation of binary numbers. A sequence of four bits can take a value from (0000)  to (1111) .
                                                                                                      2
                                                                                                               2
        In the hexadecimal system (0000)  and (1111) , are expressed as (0)  and (F) , respectively. So, a hex digit can be
                                       2
                                                                      16
                                                                               16
                                                  2
        used to represent a sequence of four binary digits (or four bits). Table 2.7 below shows the decimal, octal, and binary
        equivalent of each hexadecimal digit.
          36   Touchpad Computer Science-XI
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