Online Calculators since 2009
Binary to Decimal converter
- Convert a binary number to a decimal number
- Convert a decimal number to a binay number
Binary numbers are base 2, represented by 1 and 0, Decimal numbers are base 10 represented by numbers 0 to 9
How a Binary to Decimal Converter Can be More Efficient
A binary to decimal converter is a great help when converting a given binary number into a respective decimal number. The binary to decimal converter is very easy to use and helps you perform a range of decimal conversion of a numbers within seconds. You will get your results just after pressing "enter". It's very quick and always accurate.
Performing binary to decimal conversion is one of the most important operations in the world of digital electronics and communications. With this calculator you can perform conversions that help you read binary numbers in a more human-friendly way. Decimal numbers are the most popular and generic number system being used worldwide and as humans we find the decimal system relatively easy to work with, particularly when using the power of 10. Binary is great for computers but most humans would struggle to compute a binary math equation.
Let's take a look at the binary and decimal number system, and how can we convert a binary number into a decimal number and their importance.
Binary number system
The binary number system is a number system that uses the number '2' as its base (also known as radix). Since the base of every binary number is '2', it simply means that every binary number only consists of two numbers i.e., 0 and 1.
Use of binary number system in the digital world
The major use of this system is to perform "TRUE" or "FALSE" operation or to define the "ON" or "OFF" state. The most efficient use of this system is to detect the "ON" and "OFF" state of an electric system so binary system occur frequently in electronics and engineering calculations.
The binary number system is considered as the base of any computer system as computers take input in only two forms i.e., 0 and 1. It is also used to compose data in computer-based and computer controlled machines in a number of industries. Even this digital text that you are reading right now consists of binary number system only. This converter tool that you are going to use to convert a binary number into a decimal number will also be using the same number system to perform any operation.
How to read a binary number
Reading a binary number is not a difficult task. It is much easier than it looks. If you want to convert a binary number into a decimal number and want to understand its concept as well, you need to have a basic knowledge of this system such as how do we read a binary number, how do we represent it, etc. The binary number system is a positional system and this is the reason why every number in this system is raised to the powers of '2'. The rightmost digit will be in the position of 20.
For example, (1101)2 can be written as-
Decimal number system
This number system is the most popular and the most used number system in the world, having the number '10' as its base. There is a total of 10 numbers being used in this system i.e., from 0 to 9.
How to convert a binary number into a decimal number
There are two methods to convert a binary number into a decimal number. In the first method, the conversion is performed using the positions. The second method is known as 'Double Dabble'. The first method is the most popular one and is the most widely used. The second method is a complicated one and is used to convert longer binary string faster. We are going to discuss the most widely used one.
Converting binary numbers into decimal numbers using the positions
- The first step is to write down the number and determine the positions, namely the power of 2 that the digit belongs to.
- The next step is to represent the number in terms of its positions.
- The final step is to calculate the final number you got.
Converting binary numbers into decimal number Example
| Binary | Decimal |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
Summary
The Binary number system has become the language of computers and electronics in the modern world. It is not possible for a normal human being to understand everything that is written in binary language. This is why a binary to decimal converter is used to convert the binary numbers into decimal units so that we can understand it more efficiently. You can use this online interface anytime in order to get instant and precise results.
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