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Binary to Decimal

There are different number systems in use.Binary Number System and Decimal Number System is widely used. In computers, data are stored in binary form. That is, computers use only zero and one to represent all data. So, when a user want to view the data, the system will convert it to decimal form. So, this conversion is very important in day to day life. In this article, we will learn binary to decimal conversion.

Binary Number:

A number is said to be a binary number, when its base is 2 and it contains only two digits, 0 and 1. In binary number, each and every numbers are represented by these two digits .

Example 1: 0101 is equal to 5.

Example 2: 1111 is equal to 15.

Decimal Number:

A number is said be a decimal number, when its base is 10 and it can be written with the help of ten digits that are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. All the number can be written with the help of these ten digits.

Example 1: 41

Example 2: 551

Example 3: 674

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How to Convert Binary to Decimal

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Given below are the steps for how to convert binary to decimal -

Step 1: First, we count the number of binary digits in the given number. Let there be n numbers.

Step 2: Then, we multiply each digit with the 2n-1 , when n is equal to number of position from right side.

Step 3: Then, we add each number.

Step 4: After addition, the resultant is equal to decimal value of that binary number.

If the given number contain decimal then,

Step 1: Count the number of digits after the decimal. Let it be m.

Step 2: Then, we multiply each digit after decimal with `1/2^m` , where m is the number of position of digit from the decimal.

Step 3: Then, we add each number.

Step 4: After addition, the resultant is equal to decimal value of that binary number.

Converting Binary to Decimal

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Given below are some of the solved examples on converting binary to decimal -

Solved Examples

Question 1: Convert 1101 to decimal number?
Solution:

Binary number is 1101.

So, 1101 = (1 X 23)  + (1 X 22) + (0 X 21) + (1 X 20)

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

                  =  8 + 4 + 0 + 1

Correct answer is 13
Question 2: Convert 1001 to decimal number?
Solution:

Binary number is 1001.

So,  1001 = (1 X 23)  + (0 X 22) + (0 X 21) + (1 X 20)

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

                  =  8 + 0 + 0 + 1

Correct answer is 9
Question 3: Convert 01011101 to decimal number?
Solution:

Binary number is  01011101.

01011101 = (0 X 27)  + (1 X 26) + (0 X 25) + (1 X 24) + (1 X 23)  + (1 X 22) + (0 X 21) + (1 X 20)

                    = (0 X 128) + (1 X 64) + (0 X 32) + (1 X 16) + (1 X 8) + (1 X 4) + (0 X 2) + (1 X 1)

                    =  0 + 64 + 0 + 16 + 8 + 4 + 0 + 1

Correct answer is 93
Question 4: Convert 01100.011 to decimal number?
Correct answer is 12.375

Practice Problems

Question 1: Convert 110011 to decimal number?
Question 2: Convert 01110011 to decimal number?
Question 3: Convert 1001 to decimal number?
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