Binary to Decimal Converter

Binary to Decimal Converter is a free online tool to convert binary to decimal. Converting between binary to decimal is a common task in everyday life. Here, GeeksforGeeks provides a free user-friendly, and efficient online binary decimal Conversion tool to simplify this process and ensure accuracy. It is a fast, easy-to-use general-purpose calculator that can be used in any field such as computer science. Furthermore, it also helps students and working professionals to solve a wide range of day-to-day problems.

Binary to Decimal Converter

The binary-to-decimal converter is added below. This bin-to-dec converter is used to convert binary values to decimal values.

What is Binary to Decimal?

Binary To Decimal Conversion is used to convert the binary value to the decimal values. Binary numbers are numbers that have a base of 2 and are used in computer programming. Whereas Decimal numbers are the numbers that have a base of 10 and are used in normal day-to-day operations.

What is Binary System?

Binary System is a system of writing numbers using only two numbers that are, 0 and 1. The base of the binary number is 2. This system was first used by ancient Indian, Chinese, and Egyptian people for various purposes. The binary number system is used in electronic and computer programming.

What is Decimal System?

The Decimal Numbers System is the number system that is used by us in our daily lives. The base of Decimal numbers is 10 and it uses 10 digits that are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

How to use Binary to Decimal Calculator?

We can easily use the binary-to-decimal calculator by following the steps discussed below,

Step 1: Enter the given value in the binary input field.

Step 2: Click on the convert button to convert the binary value into the decimal value.

Step 3: The value shown as the result is the required value in the decimal form.

Binary to Decimal Formula

To convert a binary number to decimal we need to perform a multiplication operation on each digit of a binary number from right to left with powers of 2 starting from 0 and add each result to get the decimal number of it. 

Decimal Number = n^th bit × 2^n-1

Binary to Decimal Formula

n = b_nq + b_n-1q^n-2 +.........+ b₂q² +b₁q¹ +b₀q⁰ + b_-1q^-1 + b_-2q^-2 

Where,

• N is Decimal Equivalent
• b is the Digit
• q is the Base Value

How to Convert Binary to Decimal

You just have to follow the below steps to convert binary numbers to their decimal equivalent.

Step 1: Write the binary number and count the powers of 2 from right to left (starting from 0).

Step 2: Write each binary digit(right to left) with corresponding powers of 2 from right to left, such that MSB or the first binary digit will be multiplied by the greatest power of 2.

Step 3: Add all the products in the step 2

Step 4: The answer is our decimal number.

This can be better explained using the below examples.

Binary to Decimal Conversion

Binary to Decimal conversion is achieved using the two steps that are,

• Positional Notation Method
• Doubling Method

Now let's learn about them in detail.

Method 1: Using Positions

Binary to Decimal Conversion can be achieved using the example added below.

Example 1: Let's consider a binary number 1111. We need to convert this binary number to a decimal number.

As mentioned in the above paragraph while converting from binary to decimal we need to consider each digit in binary number from right to left.

By this way, we can do binary to decimal conversion.

Note: We represent any binary number with this format (xxxx)₂ and decimal in (xxxx)₁₀ format.

Example 2: Convert (101010)₂ = (?)₁₀

We keep on increasing the power of 2 as long as number of digits in binary number increases.

Example 3: Convert (11100)₂ = (?)₁₀

Resultant Decimal number = 0+0+4+8+16 = 28

So (11100)₂ = (28)₁₀

Also Check,

• Decimal to Binary Converter

Method 2: Doubling Method

To explain this method we will consider an example and try to solve that stepwise.

Example 1: Convert Binary number (10001)₂ to decimal.

Similar to the above approach, In this approach also consider each digit but from left to right and performs step-wise computations on it.

1	0	0	0	1

Step-1 First we need to multiply 0 with 2 and add the 1st digit in binary number.

0 x 2 + 1 = 0 + 1 = 1

Step-2 Now use the result of above step and multiply with 2 and add the second digit of binary number.

1	0	0	0	1

1 x 2 + 0 = 2 + 0 = 2

The same step 2 is repeated until there will be no digit left. The final result will be the resultant decimal number.

1	0	0	0	1

2 x 2 + 0 = 4 + 0 = 4

1	0	0	0	1

4 x 2 + 0 = 8 + 0 = 8

1	0	0	0	1

8 x 2 + 1 = 16 + 1 = 17

So we performed step 2 on all remaining numbers and finally, we left with result 17 which is a decimal number for the given binary number.

So (10001)₂ = (17)₁₀

Example 2: Convert (111)₂ to decimal using doubling approach.

1	1	1

0 x 2 + 1 = 0 + 1 = 1

1	1	1

1 x 2 + 1 = 2 + 1 = 3

1	1	1

3 x 2 + 1 = 6 + 1 = 7

The final result is 7 which is a Decimal number for 111 binary numeral system. So (111)₂ = (7)₁₀

These are the 2 approaches that can be used or applied to convert binary to decimal.

How to Read a Binary Number?

Binary numbers are read by separating them into separate digits. Each digit in binary is represented using 0 and 1 and they are the powers of 2 starting from left hand side and then the power is gradually increased from 0 to (n-1).

Binary to Decimal Conversion Table

The given binary to decimal conversion table will help you to convert binary to decimal.

Conclusion

In conclusion, the Binary to Decimal Calculator is a free online tool prepared by GeekforGeeks that converts the given value of the binary number system into the value of a decimal number system . It is a fast and easy-to-use tool that helps students solve various problems.

Read More,

• Decimal to Hexadecimal Converter
• Binary to Hexadecimal Converter

Binary to Decimal Conversion Examples

Example 1: Convert (111)₂ to Decimal.

Solution:

We have (111)₂ in binary

⇒ 1 ⨯ 2² + 1 ⨯ 2¹ + 1 ⨯ 2⁰

= 4 + 2 + 1 = 7

Example 2: Convert (10110)₂ to Decimal.

Solution:

We have (10110)₂ in Binary

1 ⨯ 2⁴ + 0 ⨯ 2³ + 1 ⨯ 2² + 1 ⨯ 2¹ + 0 ⨯ 2⁰

= 16 + 4 + 2 = 22

Example 3: Convert (10001)₂ to Decimal.

Solution:

We have (10001)₂ in Binary

⇒ 1 ⨯ 2⁴ + 0 ⨯ 2³ + 0 ⨯ 2² + 0 ⨯ 2¹ + 1 ⨯ 2⁰

= 16 + 0 + 0 + 0 + 1 = 17

Example 4: Convert (1010)₂ to Decimal.

Solution:

We have (1010)₂ in Binary

⇒ 1 ⨯ 2³ + 0 ⨯ 2² + 1 ⨯2¹ + 0 ⨯ 2⁰

= 0 + 8 + 2 + 0 = 10

Example 5: Convert (10101101)₂ to Decimal.

Solution:

Convert Binary to Decimal (bn to dec)

Q1: Convert (11000)₂ to Decimal.

Q2: Convert (10111)₂ to Decimal.

Q3: Convert (111110000)₂ to Decimal.

Q4: Convert (00011)₂ to Decimal.

Q5: Convert (110011)₂ to Decimal.

Also Check,

• Million to Crore
• Million to Lakhs