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

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#### 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

 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

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

Octal number
Quinary number
Decimal number
Binary number

8
2
4
6

3
2
5
4

1 only
0 or 1
1 or 2
0 only

## ASK ANY QUESTION ON Binary Number System

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