# Binary to Decimal Converter

## About Binary To Decimal Converter

The computer is believed to be a very remarkable tool that has always impressed us, from the very first version of the computer until the last modern pattern, not to forget the fact that computer languages "such as Binary and Decimal" are magnificently designed to help and ease our life-complexity.

The binary to Decimal converter is an online tool that helps in converting numbers from binary values to decimal. It is a simple and easy-to-use tool that can be used by anyone who needs to convert numbers from binary to decimal. Binary-to-decimal conversion is a common task in computer science. It's also surprisingly difficult to do by hand, which is why we have created this Binary to Decimal online converter tool for doing this conversion automatically.

## How to Use Binary to Decimal Converter Tool?

Step 1: Copy your Binary values to the clipboard.

Step 2: Access the tool

Step 3: Paste the copied Binary numbers into the toolbox manually or use the paste icon in the top left corner of the toolbox.

Step 4: Click the button **Convert**. Once you do that, the tool will convert your Binary values into Decimal and then you can copy the output and use it wherever you want.

## Why Use This Tool?

**Simplicity:**Our Binary to Decimal is simple, yet is a powerful tool.**Ease of Use:**This tool is extremely easy to use. Using this tool doesn't require going through many steps, just enter the Binary strings and hit the button Convert.**Fast Conversion:**Another benefit of this tool that is worth mentioning is this tool converts any Binary number to a Decimal value in the blink of an eye.**Clean Design:**The clean interface of this tool makes it so beautiful and adorable, even though it does the most complex equations.**Accuracy:**We have built a binary to a decimal converter that will allow you to convert any number from binary to decimal without any errors. This converter is accurate.**Free:**As for our all tools, we don't charge you anything for using this awesome tool. You can use it as much as you want and whenever you want.

## How Does Binary to Decimal Conversion Work?

Binary numbers are made up of zeros and ones, and they represent different values in the numbering system. Decimal numbers are made up of ten digits, which are either zeros or ones and represent different values in the numbering system.

For example, the number 11111 can be broken down into two groups of 4 bits: 1111 and 111. These two groups can be converted to their decimal equivalents, which are 7 and 5 respectively. This process is repeated until the entire binary number has been converted.

We can convert binary to decimal by following these steps:

- Convert each digit of the binary number to its equivalent in the decimal system.
- Add all of the decimal values together to get a sum that represents the number in decimal notation.

To apply, follow these rules.

**Rule 1:** Write down the binary number.

**Rule 2: **Begin with the (LSD- the rightmost one) least significant digit then have the digit multiplied by the value of the position, proceed doing that until you reach the most significant digit (MSD-the leftmost one)

**Rule 3:** Add the results and you are going to have the decimal equivalent of the given binary number.Approach two: double.

This method is an algorithm that can be used to convert from any given base to decimal. Here are the rules as follows;

**Step 1: **Write down the binary number. Beginning with the left you shall be doubling the previous total and adding the new digit, for example in the first step the previous total is always zero because you just start, therefore, double the total and add the leftmost digit.

**Step 2:** Double the total and add the next leftmost digit.

**Step 3:** Double the total and add the next leftmost digit, then keep doing this until you run out of digits.

**Step 4:** The results you have after adding the last digit to the previous doubled total is the decimal equivalent.

## Binary To Decimal Converter FAQs

### What is Binary?

Binary is the simplest form of encoding, and the most fundamental. It is a system that uses two symbols, 0 and 1, to encode information. This system is also known as base-2 or base-2 number system.

So, in binary, only two values are used to represent numbers. These values are 0 and 1. Numbers can be represented by these digits in the following way:

0 = 001

1 = 010

2 = 100

3 = 101

4 = 110

5 = 111

### Why do we call it the binary number system?

Because there are only two options for number representation all binary numbers are constructed from the two digits 0 and 1.

### What is Decimal?

The decimal system is a numeral system that uses base-10 arithmetic. The decimal system is the most widely used numeral system in the world and is the standard for the measurement of most real-world quantities. This system is also known as base-10 or occasionally called denary.

### How Does the Binary Number System Work?

The binary number system is the most effective part of the whole computer process which is so impressive, only the binary can fit so significantly like that to the role of inputs and outputs, therefore binary can work in an essential part of the whole computer and even represent.

### How Does the Binary Decimal System Work?

The decimal system depends on the digits within the number, for example, the first digit after the decimal shows the tenth place, meantime, the following digit after the decimal number represents the hundredths place and the remaining digits proceed to fill in the place value until there is no digit left. The binary as a system functions with only two digits, it can be represented by these two numbers (0,1). Whereas the decimal number has more and different digits than the binary for example the set number from zero to nine (0,9).

## Binary to Decimal Conversion Example:

Convert the binary number (1110010)_{2} into a decimal number:

Method 1:

(0 * 2^{0}) + (1 * 2^{1}) + (0 * 2^{2}) + (0 * 2^{3}) + (1 * 2^{4}) + (1 * 2^{5}) + (1 * 2^{6})

= (0 * 1) + (1 * 2) + (0 * 4) + (0 * 8) + (1 * 16) + (1 * 32) + (1 * 64)

= 0 + 2 + 0 + 0 + 16 + 32 + 64 = 114

Method 2:

0 (previous sum at the starting point)

(0 + 1) * 2 = 2

2 + 1 = 3

3 * 2 =6

6 + 1 =7

7 * 2 = 14

14 + 0 =14

14 * 2 = 28

28 + 0 =28

28 * 2 = 56

56 + 1 = 57

57 * 2 = 114

## Binary to Decimal Conversion Table:

BINARY NUMBER | DECIMAL NUMBER |
---|---|

0 | 0 |

1 | 1 |

10 | 2 |

11 | 3 |

100 | 4 |

101 | 5 |

110 | 6 |

111 | 7 |

1000 | 8 |

1001 | 9 |

1010 | 10 |

1011 | 11 |

1100 | 12 |

1101 | 13 |

1110 | 14 |

1111 | 15 |

10000 | 16 |

10001 | 17 |

10010 | 18 |

10011 | 19 |

10100 | 20 |

10101 | 21 |

10110 | 22 |

10111 | 23 |

11000 | 24 |

11001 | 25 |

11010 | 26 |

11011 | 27 |

11100 | 28 |

11101 | 29 |

11110 | 30 |

11111 | 31 |

100000 | 32 |

1000000 | 64 |

10000000 | 128 |

100000000 | 256 |

1000000000 | 512 |

10000000000 | 1024 |

100000000000 | 2048 |