Binary to Decimal Converter Calculator

A binary to decimal converter is an online tool designed to convert a binary number into its equivalent decimal number. This tool simplifies the process of binary-to-decimal calculations, making it both easy and hassle-free for us. By just entering a binary number, we can quickly get its decimal equivalent. The binary to decimal converter is widely used in various fields such as computer science, where it helps programmers convert binary data into a human-readable decimal format. It is also used in digital electronics for interpreting binary codes used in circuits. Additionally, this tool can be used in mathematics to understand number system conversions, in networking for tasks like subnetting and IP address calculations, and in education as a resource for students learning about binary and decimal systems. In case, you are wondering about these number systems, we have covered these topics in the subsequent sections of our website:

What is a Binary Number System?

A binary number is a number represented in the binary system, also known as the base-2 numeral system. This system uses only two symbols: 1 (one) and 0 (zero), and it operates on positional notation with a base or radix of 2. Binary numbers are essential in computer applications, as all coding languages like C, C++, and Java rely on binary digits (0 and 1) to create programmes and encode digital data. 

For example, the binary number 10102 is converted to decimal as 1 x 23 + 0 x 22 + 1 x 22 + 0 x 20 = 10102.

What is a Decimal Number System?

The decimal number system, also known as the base-10 system, represents numbers using base 10 and is referred to as decimal notation. It consists of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit in the system has a positional value, where every digit is ten times more significant than the one to its right. This number system is widely used in computer applications and everyday life. 

Examples of decimal numbers include (45)10,(678)10, (1200)10,(89.45)10,(3.141)10.

How to Convert Binary to Decimal?

Binary to decimal conversion allows us to convert large binary numbers into a form that is easily understood by humans. There are two primary methods to perform this conversion: the Positional Notation Method and the Doubling Method. Let us know more about each method in detail.

Positional Notation Method

In the positional notation method, the value of a digit in a binary number is determined by its position, weighted by powers of 2. Follow these steps:

• Multiply each binary digit, starting from the rightmost digit, by powers of 2. Begin with 20 and increase the exponent by 1 for each digit as you move to the left.

• Add the results of all these products. The total represents the decimal equivalent of the binary number.

Binary to Decimal Conversion Using the Doubling Method

The doubling method involves repeatedly doubling the current value and adding the next binary digit. The steps are as follows:

• Start with 0 as the initial value.

• For each binary digit, double the current value and add the binary digit to it.

• Repeat this process for all digits from left to right to find the decimal equivalent.

Binary to Decimal Conversion Formula

To convert a binary number to its decimal equivalent, we use the following general formula:

(Decimal Number)10 = (d0 x 20) + (d1 x 21) + (d2 x 22) + …………. + (dn-1 x 2n-1)

where, 

• dn​ represents the digits of the binary number, starting from the rightmost digit (least significant digit) to the leftmost digit (most significant digit)

• n represents the number of digits

Let us look at some of the binary to decimal conversion examples to understand the concept better:

Example 1: Convert 101012 to decimal

Let us apply the formula to convert the binary number 101012​ into its decimal equivalent:

(Decimal Number)10 = (1x20) + (0 x 21) + (1 x 22) + (0 x 23) + (1 x 24)

                                     = 1 + 0 + 4 + 0 + 16

                                     = 21

Therefore, 101012 = 2110

Example 2: Convert 111012​ to Decimal

Let us apply the formula to convert the binary number 111012​ ​ into its decimal equivalent:

(Decimal Number)10 = (1x24) + (1 x 23) + (1 x 22) + (0 x 21) + (1 x 20)

                                     = 16 + 8 + 4 + 0 + 1

                                     = 29

Therefore, 111012 = 2110

Alternatively, we can also use binary to decimal calculators available online to save time and enhance the accuracy of the calculations.

Binary to Decimal Conversion Table

Let us look at the binary to decimal conversion of the first 30 decimal numbers provided in the table below:

In a Nutshell

The binary to decimal converter serves as a practical and efficient tool for converting binary numbers into their decimal equivalents. Understanding the concept of binary to decimal conversion can enhance our logical thinking and problem-solving abilities, especially in computer science and mathematics. Whether we are a student learning about binary and decimal systems or a professional working with data, we can use this converter as a reliable resource to ensure accuracy and efficiency in everyday tasks involving number system conversions.

FAQs

What is binary to decimal conversion?

Binary to decimal conversion is the method of converting binary numbers, made up of only 0s and 1s, into decimal numbers, which are based on the base-10 system.

How to convert binary to decimal?

You can convert binary to decimal by using the formula - (d0 x 20) + (d1 x 21) + (d2 x 22) + …………. + (dn-1 x 2n-1), where d stands for the binary digits.

How to convert 10101 binary to decimal?

By using the formula (d0 x 20) + (d1 x 21) + (d2 x 22) + …………. + (dn-1 x 2n-1), 10101 binary can be converted to decimal 2110.

What is 45 in binary form?

The binary form of 45 is 101101.

How to convert 11011 binary to decimal?

By using the formula (d0 x 20) + (d1 x 21) + (d2 x 22) + …………. + (dn-1 x 2n-1), 11011 binary can be converted to decimal 2710.

How to convert 11001 binary to decimal?

By using the formula (d0 x 20) + (d1 x 21) + (d2 x 22) + …………. + (dn-1 x 2n-1), the 11001 binary can be converted to decimal 2510.