Page 39 - Computer Science Class 11 Without Functions
P. 39

Table 2.7: Decimal, Octal and Binary (4 bits) equivalents of Hexadecimal digits

                           Hexadecimal 1         Decimal             Octal        Binary representation
                               Digit         representation     representation           (4 bits)
                                 0                  0                  0                  0000
                                 1                  1                  1                  0001
                                 2                  2                  2                  0010
                                 3                  3                  3                  0011
                                 4                  4                  4                  0100
                                 5                  5                  5                  0101
                                 6                  6                  6                  0110

                                 7                  7                  7                  0111
                                 8                  8                 10                  1000
                                 9                  9                 11                  1001
                                 A                 10                 12                  1010
                                 B                 11                 13                  1011
                                 C                 12                 14                  1100
                                 D                 13                 15                  1101
                                 E                 14                 16                  1110
                                 F                 15                 17                  1111

            Consider the number (2AE.C8) . Its symbol value and positional value are illustrated in Table 2.8.
                                       16
                                      Table 2.8: Face value and place value of digits of an octal number
                                                                                           -1
                                                                                                         -2
                                                            1
                                                                         0
               Digit's place value         16  (=256)    16  (=16)     16  (=1)          16  (=   1  )  16  (=   1  )
                                             2
                                                                                               16            256
               hex digit                       2             A            E        .         C             8
               Face value                      2            10           14        .        12             8
               Value represented by digit   2 × 16 2      10 × 16 1    14 × 16 0          12 × 16 -1    8 × 16 -2
            The computation of decimal value of (2AE.C8)  is shown below:
                                                     16
                (2AE.C8)
                       16
                               1
                       2
                                                -1
                                       0
                = 2 × 16  + A × 16  + E × 16 + C × 16 + 8 × 16 -2
                = 2 × 256 + 10 × 16 + 14 + 0.75 + 0.03125
                = 512 + 160 + 14 + 0.75 + 0.03125
                = 686.78125
            Application of Hexadecimal Numbers

            We describe three important uses of hexadecimal numbers:
            ●  Hexadecimal numbers have been used for developing software for microprocessor kits as it is easy to describe the
              addresses and names of registers using hexadecimal notation.
            ● Hexadecimal numbers find use in describing the network addresses (to be discussed in a later chapter).
            ●  Hexadecimal numbers are also used to represent colour codes in digital form. Each colour comprises three primary
              colours: red, green and blue (also referred to as RGB). A number between 0 and 255 expresses the intensity of each
              colour, often expressed as a two-digit hexadecimal number between 00 and FF. Thus, if red and green colours are
              present in full intensity and the blue colour is absent, the intensity triplet (R, G, B) would be expressed as (FF, FF, 00)
              in the hexadecimal system or as (255, 255, 0) in the decimal system.


                                                                            Number Systems and Encoding Schemes  37
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