Notes on Binary Number System | Grade 7 > Compulsory Maths > Operation on Whole Numbers | KULLABS.COM

Binary Number System

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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

= 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:



  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.
.

Very Short Questions

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

0%
  • ______ system consists of two digits 0 and 1 and its base is 2.

    Octal number
    Binary number
    Quinary number
    Decimal number
  • We must divide the given number successively by ______  in order to convert decimal number into binary number.

    6
    2
    4
    8
  • In order to convert a binary number into a decimal, it is expanded in the power of ______.

    4
    2
    5
    3
  • Each digit or bit in binary number system can be _____.

    0 only
    1 only
    0 or 1
    1 or 2
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