Page 35 - Computer Science Class 11 With Functions
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system. For example, in the numbers 234, 6249, and 5482, the symbol 4 denotes the values four, forty, and four
            hundred, respectively. Thus, the decimal number system is a positional number system. We already know that the
            decimal representation of a number comprises a string of symbols, each symbol being a decimal digit that takes one of
            the values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The value of a symbol within a number depends on its relative position addition.
            Each symbol (also called a decimal digit) within a number has an associated place value, as described below:
               Face Value: The value of a symbol in the number system is called its face value. Thus, in the decimal system, the
              symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 have the face values zero, one, two, three, four, five, six, seven, eight, and nine,
              respectively.
               Place Value: In decimal number systems, the value of a digit within a number depends on the position of the digit.
              For example,
              ○ The rightmost digit is called the one's digit or unit digit (value 10 = one),
                                                                          0
              ○ The second digit from the right end is called the tens digit (value 10  = ten),
                                                                            1
                                                                               2
              ○ The third digit from the right end is called the hundreds digit (value 10  = hundred),
                                                                                 3
              ○ The fourth digit from the right end is called the thousands digit (value 10  = thousand),
                                                                                  4
              ○ The fifth digit from the right end is called the ten thousand digit (value 10  = ten thousand),
                                                                                       5
              ○ The sixth digit from the right end is called the hundred thousand digit (value 10  = hundred thousand),
                                                                                6
              ○ The seventh digit from the right end is called the millions digit (value 10  = million), and so on.
              Now, consider the number 1352. In this number,
              ○ Digit 2 represents 2 units (2 × 1)
                                             1
              ○ Digit 5 represents 5 tens (5 × 10 )
              ○ Digit 3 represents 3 hundreds (3 × 10 )
                                                 2
                                                  3
              ○ Digit 1 represents 1 thousands (1 × 10 )
            Hence the numeric value represented by the number 1352 can be calculated as:
                            2
                                            0
                                    1
                   3
              1 × 10 + 3 × 10  + 5 × 10  + 2 × 10
              = 1 × 1000 + 3 × 100 + 5 × 10 + 2 × 1 = (1352)
                                                      10
            Table 2.1 shows the digit's place value, face value, and value represented by the decimal number (1352) .
                                                                                                        10
                                   Table 2.1: Digit's place value, face value, value represented by (1352) .
                                                                                           10
                    Digit's place value  thousand (1000)  hundred (100)        ten (10)           Unit (1)
                   Digit                      1                 3                 5                 2
                   Face value                 1                 3                 5                 2
                   Value  represented      1 × 10 3           3 × 10 2          5 × 10 1          2 × 10 0
                   by digit



                     1.  Give the face value of each occurrence of the digit 4 in the number 284849.
                     2.  Give the place value of each digit in the number 284849.


            In the number 1352, digit 1 has the highest place value, it is known as Most Significant Digit (MSD). Similarly, as digit
            2 carries the minimum place value, so it is known as Least Significant Digit (LSD). In general, in a positional number
            system, the leftmost digit is the most significant, and the rightmost digit is the least significant digit.
            Now, let us look at fractional numbers. A fractional number consists of an integer part (also called an integral part)
            and a fraction part (also called a fractional part). Note that 0<= fraction part<1. A dot called a radix point separates
            the integer part from the fractional part. We have seen that while representing the whole numbers in the positional


                                                                            Number Systems and Encoding Schemes  33
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