Binary Number System

Subject: Compulsory Maths

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Overview

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. It also provides the information about the Conversion of binary numbers to decimal number, Conversion of decimal number to binary number and Alternative method fo binary number system.
Binary Number System

Binary number system

source: www.mathsisfun.com Fig: Binary Number System
source: www.mathsisfun.com
Fig: 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

source: javarevisited.blogspot.com Fig: Binary Number into Decimal Number
source: javarevisited.blogspot.com Fig: Binary Number into 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

Scholarships after +2 Abroad Studies Opportunities

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

Conversion of decimal number to binary number

source: www.slideshare.net Fig: Decimal Number into Binary Number
source: www.slideshare.net
Fig: Decimal Number into 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

25 24 23 22 21

20

32 16 8 4 2 1
1 1 1 1 0

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.
Videos for Binary Number System
Binary Numbers and Base Systems as Fast as Possible
Questions and Answers

Solution:

1110= 1 × 2+ 1 × 22 + 1 × 21 + 0 × 20
= 1 × 8 + 1 × 4 + 1 × 2 + 0
= 8 + 4 + 2 
= 14 
∴ 1110= 14

Solution:

101101= 1 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 22 
= 1 × 32 + 0 + 1 × 8 + 1 × 4 + 0 + 1 × 1 
= 32 + 8 + 4 + 1
= 45
∴ 1011012  = 45

Solution:

25 24 23 22 21 20
32 16 8 4 2 1
  1 1 0 0 1

25 = 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1
= 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20
= 11001
∴ 25 = 110012

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