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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

