Basic HTML Version

|  | Table of Contents |  | View Full Version

Page 10 - 2505_CoreGPT(Podar)_Flipbook_C7
P. 10

    DECIMAL NUMBER SYSTEM

                      The decimal number system is a standard number system for denoting numbers. It consists
                      of ten digits from 0 to 9. Only these digits can be used to represent numeric value in decimal

                      number system. Hence, the base of decimal number system is 10. The decimal number system is
                      the most widely used number system. The value represented by individual digit depends on the
                      weight and position of the digit in the number.
                      The position of the first digit towards left side of the decimal point is 0. The position of second

                      digit towards left side of the decimal point is 1. Similarly, the position of the first digit towards
                      right side of decimal point is –1. The position of second digit towards right side of decimal point
                      is –2 and so on.

                      The place value of the digits according to position and weight is as follows:

                                 Position          2           1          0                      –1         –2
                                                     2          1          0          •           –1          –2
                                 Weight           10          10         10                     10         10

                      The value of a number is determined by multiplying the digits with the weight of their position
                      and adding the results. This method is known as expansion method. The right-most digit

                      of the number has the lowest weight. This digit is called Least Significant Digit (LSD). The
                      left-most digit of a number has the highest weight. This digit is called Most Significant Digit
                      (MSD). For example, digit 7 in the number 724 is the most significant digit and 4 is the least
                      significant digit.

                      The following table shows positional weight of decimal number (724) .
                                                                                               10
                                  Place Value          Weights         Real Value of Each Digit         Units

                                Hundreds                  10 2                  7 × 10 2                 700

                                Tens                      10 1                  2 × 10 1                 20
                                Units                     10 0                  4 × 10 0                  4

                      In this table:
                                                                   2
                          The hundreds place has a weight of 10  (100), so the real value is 7 × 100, resulting in 700.
                                                             1
                          The tens place has a weight of 10  (10), so the real value is 2 × 10, resulting in 20.
                                                              0
                          The ones place has a weight of 10  (1), so the real value is 4 × 1, resulting in 4.
                      Adding these results together gives the total value of 724.

                            BINARY NUMBER SYSTEM

                      Computers are made up of tiny parts like transistors, which act as switches that can either be
                      ON or OFF, corresponding to two voltage levels. These two states are represented using the
                      numbers 0 and 1, known as binary digits or "bits."

                     8      Premium Edition-VII

| 5 6 7 8 9 10 11 12 13 14 15 |