Page 61 - Computer Science Class 11 Without Functions
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0
                                                         –1
                                           1
                                    2
                             3
                      4
                = 1 × 2  + 0 × 2  + 0 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 –2
                                      1
                = 16 + 0 + 0 + 2 + 1 + 0 +
                                      4
                = 19 + 0.25
                = 19.25
                = (10011.01)  = (19.25) 10
                           2
            b.  (C25.D2)  to decimal number.
                       16
                Face Value         C     2      5  .   D    2
                                                       –1
                                           1
                                                0
                                    2
                Place value       16    16   16   .  16   16 –2
                               1
                                       0
                       2
                                                –1
                = C × 16  + 2 × 16  + 5 × 16 + D × 16 + 2 × 16 –2
                                         13    2
                = 12 × 256 + 2 × 16 + 5 × 1 +    +
                                         16   256
                = 3072 + 32 + 5 + 0.812 + 0.007
                = 3109.819
                = (C25.D2)  = (3109.819) 10
                         16
            c.  (157.25) to decimal number.
                       8
                Face Value         1     5      7  .  2     5
                Place value        8    2  8  1    8  0    8  –1    8 –2
                      2
                                           –1
                                    0
                             1
                = 1 × 8  + 5 × 8  + 7 × 8 + 2 × 8 + 5 × 8 –2
                              2
                = 64 + 40 + 7 +   +   5
                              8  64
                       2
                = 111 +   +   5
                       8   64
                = 111 + 0.25 + 0.07
                = 111.328
                Hence, (157.25)  = (111.328) 10
                              8
            d.  (0.341) to hexadecimal till 3 digits after the radix point.
                      10
                                           Fraction part     Integer part
              0.341   × 16  =  5.456          0.456               5
              0.456   × 16  =  7.296          0.296               7

              0.296   × 16  =  4.736          0.736               4
              (0.341)  = (.574) 16
                     10
            2.6 Encoding Schemes

            We have studied various number systems that enable us to deal with numeric data. Besides numbers, computers also
            deal with other forms of data like the text of characters, speech, images, and signals from various equipment such
            as ECG, MRI, radars, satellites, and mobiles. However, besides numbers, the text is the most common form of input
            to computers and the most common form of output produced by computers. As the text comprises characters, we
            will study the representation of characters in this section. As the computer needs to distinguish between different
            characters, a unique code is assigned for each character. A mapping of the characters to their unique codes is called an
            encoding scheme. When a key is pressed on the keyboard, it is internally mapped to a unique code.
            Several encoding schemes have evolved over the years, for example, ASCII and UNICODE. India has also developed the
            Indian Script Code for Information Interchange (ISCII) — a coding scheme for representing characters in various writing
            systems in India.



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