# How to Binary to Decimal?

In this article, we will teach you **how to convert binary to decimal?** Binary to decimal conversion is done by converting a given number in the binary number system to its equivalent value in the decimal number system. A number system is a format for representing numbers in a certain way. The **binary number system** is used in computers and electronic systems to represent data and consists of only two digits which are 0 and 1. **Decimal number system** is the most widely used number system in the world which can be easily understood by the people. It consists of digits from 0 to 9. Binary to decimal conversion can be performed in the simplest way by adding the products of each binary digit to it.

## What is binary to decimal convert?

Binary to decimal conversion is done to help large binary numbers be easily read in a form that humans can understand. Every number system has a base and the base of a number system is determined by the total number of digits used in it.

**For example**, the base of the binary number system is 2 because it has only two digits to represent. Similarly, the base of the decimal number system is 10, as it takes 10 digits to represent a number. The binary number system that uses only two digits 0 and 1 is the most familiar number system for decimal numbers in general. Its base is 10 with only 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

**Convert binary to decimal formula:**

The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n):

## Methods of conversion from binary to decimal number system:

Here we have mainly described two methods to convert a binary number to a decimal number which are given below:

- Positional Notation Method
- Doubling Method

### 1 : Positional Notation Method

Using this method, write down the powers of two from **right to left**. Start at **2 ^{0}**, evaluating it as “

**1**“. Increment the exponent by one for each power. Stop when the amount of elements in the list is equal to the amount of digits in the binary number.

**Example:**

- The example of number
**10011011**, has eight digits, so the list, with eight elements, would look like this:**128, 64, 32, 16, 8, 4, 2, 1**

- Add up the numbers written below the line. Here’s what you do:
**128 + 0 + 0 + 16 + 8 + 0 + 2 + 1 = 155**. This is the decimal equivalent of the binary number**10011011**.

- Finally, write the answer along with its base subscript look like:
**155**_{10}

2 : Doubling Method

Using this method does not use up the powers. To convert binary integer to decimal, the leftmost digit has to be started by adding 0.

**Example:**

- Let’s say the number you are working with is
**1011001**. Write it as given in the image._{2}

- Start by adding the
**left-most digit****is 1**, Next,**multiply this by 2**, and**add the next digit in your number**(as you progress from left to right) to this product.

- Since you are working with the binary number
**1011001**, your first digit on the left is_{2}**1**. Your**previous total is 0**because you haven’t started yet. You must double the previous total, add 0, and 1 to the current digit. 0 x 2 + 1 = 1, so your new current sum is 1.

- Double your current total and add the next leftmost digit.
**Your current total is now 1**and the**new current digit is 0**. So,**double 1 and add 0**. to do that:**1 x 2 + 0 = 2**. Your new current total is**2**.

- Just keep going. Next, double your current total, and add 1, your next digit.
**2 x 2 + 1 = 5**. Your current total is now 5.

- Continue repeat the previous step.

- Repeat the previous step again and again until you’ve run out of digits.

- You’re all done! You’ve converted
**1011001**to decimal notation to its decimal form,_{2}**89**.

That’s all on **how to binary to decimal?** when you convert your binary number to decimal then read above methods. Here, we have provided two methods that you can try out. hope thsi is helpful to you.