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    NUMBER SYSTEM

                      A Number System is simply a method of counting. There are many number systems in existence.

                      Consider a clock. Clocks have 24 hours, each hour composed of 60 minutes. Each minute is in turn
                      composed of 60 seconds. When you learnt to count, you used the numbers, like 1, 2, 3, etc. Similarly,
                      computers also have their own number system, known as the binary number system.

                      The digital computer represents all kinds of data and information like audio, graphics, video, text and
                      numbers in binary form. The total number of digits used in a number system is called its base or radix.
                      Therefore, when someone says that they are working with number system of radix 2, it means base 2,
                      i.e., binary number system. The base is written after the number as subscript such as (512) . In this
                                                                                                                  10
                      example, the number 10 is written as the subscript to express the number in decimal number system.
                      There are four types of number systems, which are as follows:

                         1.  Decimal number system                            2.  Binary number system

                         3.  Octal number system                              4.  Hexadecimal number system

                      The decimal number system is used in general. However, the computers use binary number system.
                      The octal and hexadecimal number systems are also used in the computer.

                           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.

                      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 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). 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
                                                                Hundreds             Tens              Units

                              Weights                              10 2               10 1              10 0

                              Real Value of each digit            7 × 10 2          2 × 10 1          4 × 10 0
                              Result                               700                20                 4

                       8    Premium Edition-VII

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