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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)10. In this
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
Hundereds 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
Binary Number System
The word binary comes from 'Bi-' meaning two. We see 'bi-' in words such as ‘bicycle‘
(two wheels) or ‘binocular’ (two eyes). The binary numbers have the base of 2.
8 Play (Ver. 2.0)-VIII

