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# Binary To Decimal Converter

To convert input binary number using binary to decimal converter

Table of Contents:

## Binary to Decimal Converter

Binary to Decimal Converter is an online tool that helps to convert binary numbers into decimal numbers.

## What is the Binary Number system?

In this system, numbers are used in binary form and it is also based on the 2-number system. It contains the element only “`0 and 1`

” and its domain set can be written as the `{0, 1}`

.

Moreover, Binary number system plays an exclusive role in computer programming and every number in this system is referred to as the bit.

## What is a Decimal Number system?

This system is based on the **10** numeral system and contains the number of digits from “**0 to 9**”. The set of the numbers can be stated as the {**0, 1, 2, 3, 4, 5, 6, 7, 8, 9**} and it plays an important role in our daily life use.

## Steps to Convert Binary to Decimal Number

Follow the below steps to convert the number from binary to decimal.

- First, write the binary number and count the number to move from right to left. Then place the value in the exponent of 2 (power starts from zero) for non-decimal numbers and for decimal numbers power starts from “-1” and so on after the decimal point to move from left to right.
- Write each binary digit with its corresponding power of 2 to move from right to left.
- Solve all powers and add the products.
- Then final answer is the required decimal number.

**Example 1:**

Convert the “**101011**” into a Decimal number.

**Solution**

**Step 1: **Write the given binary number.

= 101011

**Step 2: **Place the digit value in the exponent of “2” with the multiple of its digit and simplify.

(101011)_{2}= (1** ×** 2⁵) + (0** ×** 2⁴) + (1** ×** 2³) + (0** ×** 2²) + (1** ×** 2¹) + (1** ×** 2⁰)

=(1** ×** 32) + (0** ×** 16) + (1** ×** 8) + (0** ×** 4) + (1** ×** 2) + (1** ×** 1)

Multiply all terms and add them to get the final answer.

= (32) + (0) + (8) + (0) + (2) + (1)

= 32 + 0 + 8 + 0 + 2 + 1

= 32 + 8 + 2 + 1`(101011)`

_{2} = (43)_{10}

**Example 2:**

Convert the given binary number “**1011.11**” into the decimal number.

**Solution**

**Step 1: **Write the given binary number.

= 1011.11

**Step 2: **Place the digit value in the exponent of “**2**” with the multiple of its digit and simplify.

(1011.11)_{2} =(1** ×** 2³) + (0** ×** 2²) + (1** ×** 2¹) + (1** ×** 2⁰) + (1** ×** 2⁻¹) + (1** ×** 2⁻²)

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

Multiply all terms and add them to get the final answer.

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

= 8 + 0 + 2 + 1 + 0.5 + 0.25

= 8 + 2 + 1+ 0.5 + 0.25`(1011.11)`

_{2} = (11.75)_{10}

**References: **

- Binary number system | Khan Academy.
- What is Decimal number system? | Encyclopedia Britannica.
- Method to convert binary to decimal | Networking.