Table of Contents

# INTRODUCTION

So, hey guys in today’s blog we’ll discuss **“how to convert binary to decimal number system”**.

Before we start, let take a recap about binary and decimal number:

In the **Binary Number system**, It uses only two numbers **“0”** and **“1”**. Its base is** 2**. Example are:- 1001, 110011, 10101010, 11000010, etc. these type of number are known as binary numbers. On the other hand, the **Decimal Number system** uses the digit **0 to 9 (0,1,2,3,4,5,6,7,8,9)** and its base is **10**. Example – 354,5610, 678910, 7810. 85120 etc. these numbers are decimal numbers.

For more detail go to this link** “Computer Number System”**

Now, let discuss how to calculate

## How To Convert Binary to Decimal Number System

For more clarify, let start with the example

**Binary to Decimal**

**Example 1**: Convert binary number **1010** into decimal number?

Sol: 1 x 2^{3} = 8

0 x 2^{2} = 0

1 x 2^{1} = 2

0 x 2^{0} = 0

Now, sum all the outputs

= 8+0+2+0 = 10

Hence, the decimal number is **10 _{10}**

**Example 2** : Convert binary number **101010** into binary number?

Sol: 1 x 2^{5} = 32

0 x 2^{4} = 0

1 x 2^{3} = 8

0 x 2^{2} = 0

1 x 2^{1} = 2

0 x 2^{0} = 0

Now, sum all the outputs

=32+0+8+0+2+0 = 42

Hence, the decimal number is** 42 _{10}**

**Example 3**: convert binary number **11011** into decimal number?

Sol: 1 x 2^{4} = 16

1 x 2^{3} = 8

0 x 2^{2} = 0

1 x 2^{1} = 2

1 x 2^{0} = 1

Now, sum all the outputs

= 16+8+0+2+1 = 27

Hence, the decimal number is** 27 _{10}**

**Example 4**: Convert binary number **01010110 **into decimal number?

Sol: 0 x 2^{7} = 0

1 x 2^{6} = 64

0 x 2^{5} = 0

1 x 2^{4} = 16

0 x 2^{3} = 0

1 x 2^{2} = 4

1 x 2^{1} = 2

0 x 2^{0} = 0

Now, sum all the outputs

=0+64+0+16+0+4+2+0 = 86

Hence, the decimal number is 86_{10}

These are the without decimal point questions, but now we are going to solve the decimal point binary number into decimal like 100.01, 0100.11 into decimal.

**Example 5**: Convert binary number **1001.01** into decimal?

Sol: 1 x 2^{3} = 8

0 x 2^{2} = 0

0 x 2^{1} = 0

1 x 2^{0} = 1

.0 x 2^{-1} = 0

.1 x 2^{-2} = 1 x 1/4 = 1/4

Now, sum all the ouputs

8+0+0+1+0+1/4 = (32+4+1)/4

= 37/4 = 9.25

Hence, the decimal number is **9.25 _{10}**

**Example 6**: Convert binary number **01.101** into decimal?

Sol: 0 x 2^{1} = 0

1 x 2^{0} = 1

.1 x 2^{-1} = 1/2

.0 x 2^{-2} = 0

.1 x 2^{-3} = 1/8

Now, sum all the outputs

0+1+1/2+0+1/8 = (8+4+1)/8

= 13/8 = 1.625

Hence, the decimal number is** 1.625 _{10}**

The method I used in this blog to calculate binary to decimal number is **“Positional notation method”**. I hope you like this method, if you want to calculate with other method so let me know in the comment section. For, now I am giving some practice question for you guys so that you can easily solve any question of binary to decimal converting value.

**Practice Questions:**

-Convert all these numbers into decimal.

**101**(Ans 5)**0011**(Ans 3)**101100**(Ans 4)**1000011**(Ans 67)**110111**(Ans 55)**10.1**(Ans 2.5)**101.10**(Ans 5.5)**111.010**(Ans 7.25)**001.01**(Ans 1.25)**101110.11**(Ans 46.75)

I am also provide you the answer so that it will help to recheck your answer.

## Conclusion:

I have told you that how to convert binary to decimal. If you do not understand, then tell me in the comment section so that I come with a new method for you. And if you have difficulty in solving any part of my given practice question, then you can also ask me in the comment section.

In the upcoming blog, we will see **how to convert decimal numbers to binary**. Till then, you read our old blog and tell us about your favorite topic which you want to know.

I hope you guys like our blog, keep learning with computerstudypoint 😊