# 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

Binary to Decimal

Example 1: Convert binary number 1010 into decimal number?

Sol: 1 x 23 = 8

0 x 22 = 0

1 x 21 = 2

0 x 20 = 0

Now, sum all the outputs

= 8+0+2+0 = 10

Hence, the decimal number is 1010

Example 2 : Convert binary number 101010 into binary number?

Sol: 1 x 25 = 32

0 x 24 = 0

1 x 23 = 8

0 x 22 = 0

1 x 21 = 2

0 x 20 = 0

Now, sum all the outputs

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

Hence, the decimal number is 4210

Example 3: convert binary number 11011 into decimal number?

Sol: 1 x 24 = 16

1 x 23 = 8

0 x 22 = 0

1 x 21 = 2

1 x 20 = 1

Now, sum all the outputs

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

Hence, the decimal number is 2710

Example 4: Convert binary number 01010110 into decimal number?

Sol: 0 x 27 = 0

1 x 26 = 64

0 x 25 = 0

1 x 24 = 16

0 x 23 = 0

1 x 22 = 4

1 x 21 = 2

0 x 20 = 0

Now, sum all the outputs

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

Hence, the decimal number is 8610

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 23 = 8

0 x 22 = 0

0 x 21 = 0

1 x 20 = 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 9.2510

Example 6: Convert binary number 01.101 into decimal?

Sol: 0 x 21 = 0

1 x 20 = 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 1.62510

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.

1. 101 (Ans 5)
2. 0011 (Ans 3)
3. 101100 (Ans 4)
4. 1000011 (Ans 67)
5. 110111 (Ans 55)
6. 10.1 (Ans 2.5)
7. 101.10 (Ans 5.5)
8. 111.010 (Ans 7.25)
9. 001.01 (Ans 1.25)
10. 101110.11 (Ans 46.75)