Binary Number System

Binary number system

Binary number system consists of two digits 0 and 1 and its base is 2. Each digit or bit in binary number system can be 0 or 1. Digital computer represents all kinds of data and information in the binary system.

Conversion of binary numbers to decimal number

110011₂ = 1× 2⁵ + 1× 2⁴ + 0× 2³ + 0× 2² + 1× 2¹ + 1× 2⁰In order to convert a binary number into a decimal, it is expanded in the power of 2. Then by simplifyingthe expanded form of the binary number, we obtain a decimal number. For example,
1011₂ = 1× 2³ + 0× 2² + 1× 2¹ + 1× 2⁰
= 8 + 0 + 2 + 1
∴ 1011₂ = 11

= 32 + 16 + 0 + 0 + 2 + 1
∴ 110011₂ = 51

Conversion of decimal number to binary number

We can convert decimal number into a binary number by using the place value table of the binary system. For example:
Convert 30 into binary system

From the table:
or, 30 = 1× 16 + 1× 8 + 1× 4 + 1× 2 + 1× 1
or, 30 = 1× 2⁴ + 1× 2³ + 1× 2² + 1× 2¹ + 1× 2⁰
∴ 30 = 11110₂

Alternative method
We must divide the given number successively by 2 in order to convert decimal number into binary number. The remainder obtained in each successive division is listed in a separate column. For example:

Things to remember

1. Binary number system consists of two digits 0 and 1 and its base is2.
2. Each digit or bit in binary number system can be 0 or 1.
3. Digital computer represents all kinds of data and information in the binary system.

• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.

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