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means base 2, i.e., binary number system. The base is written after the number as subscript such
as (512) . In this example, the number 10 is written as the subscript to express the number in
10
decimal number system. We say it as 512 with base 10.

Extra Bytes

• The numerical digits, we use today, i.e., 1, 2 and 3 are based on the Hindu-Arabic numeral
system.
• Different names for the number 0 include zero, nought, naught, nil, zilch and zip.

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
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 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 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) . The
digit 7 in the number 724 is the most significant digit and 4 is the least significant digit.
The given 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

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.
A computer is a machine made up of transistors, switches and other components. All these
electronic components are in two mutually exclusive states, either ON or OFF. The two binary
digits represent these two states. Every instruction given to a computer is converted into 0’s and
1’s so that it can be understood and implemented by the computer. Binary language is therefore
known as the machine language .

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