Page 9 - TP_Prime_V2.2_Class7
P. 9

The digital computer represents all kinds of data and information like audio, graphics, video,

 01              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 a number

                 system of radix 2, it means the base is 2, that is, the binary number system. The base is
                 written after the number as subscript such as (512) . In this example, the number 10 is
                                                                            10
                 written as the subscript to express the number in decimal number system.
                 There are four types of number systems:

                 1.  Decimal number system               3.  Octal number system
                 2.  Binary number system                4.  Hexadecimal number system

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


                  Decimal Number System


                 The decimal number system is a standard number system for denoting numbers. It consists                   7
                 of ten digits from 0 to 9. Only these digits can be used to represent any 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 the left side of the decimal point is 0. The position
                 of the second digit towards the left side of the decimal point is 1. Similarly, the position of

                 the first digit towards the right side of the decimal point is –1. The position of the second
                 digit towards the right side of the decimal point is –2, and so on.
                 The place value of the digits is determined by their position and weight as follows:


                   Position           2             1            0                            –1            –2
                   Weights           10 2          10 1         10 0            .            10 –1         10 –2

                 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). The 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
   4   5   6   7   8   9   10   11   12   13   14