Subject:

- Binary to Decimal Converter
- Decimal to binary conversion table
- Binary to decimal conversion result in base numbers
- Binary System
- Decimal System
- Decimal System
- Binary-coded Decimal
- How to Read a Binary Number
- How to Convert Binary to Decimal
- AS SEEN ON.
- Method 1: Using Positions
- Method 2: Double Dabble
- Related Calculators:

## Binary to Decimal Converter

In order to use this new **binary to decimal converter** tool, type any binary value like 1010 into the left field below, and then hit the Convert button.

## Decimal to binary conversion table

You can see the result in the right field below. It is possible to convert up to 63 binary characters to decimal.

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### Binary to decimal conversion result in base numbers

## Binary System

The **binary numeral system** uses the number 2 as its base (radix).

As a base-2 numeral system, it consists of only two numbers: 0 and 1.

While it has been applied in ancient Egypt, China and India for different purposes, the binary system has become the language of electronics and computers in the modern world.

## Decimal System

This is the most efficient system to detect an electric signal’s off (0) and on (1) state. It is also the basis for binary code that is used to compose data in computer-based machines. Even the digital text that you are reading right now consists of binary numbers.

Reading a binary number is easier than it looks: This is a positional system; therefore, every digit in a binary number is raised to the powers of 2, starting from the rightmost with 2^{0}.

In the binary system, each binary digit refers to 1 bit.

## Decimal System

**The decimal numeral system** is the most commonly used and the standard system in daily life.

It uses the number 10 as its base (radix). Therefore, it has 10 symbols: The numbers from 0 to 9; namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

As one of the oldest known numeral systems, the **decimal numeral system** has been used by many ancient civilizations.

The difficulty of representing very large numbers in the decimal system was overcome by the Hindu–Arabic numeral system.

## Binary-coded Decimal

The Hindu-Arabic numeral system gives positions to the digits in a number and this method works by using powers of the base 10; digits are raised to the n^{th} power, in accordance with their position.

For instance, take the number 2345.67 in the decimal system:

- The digit 5 is in the position of ones (10
^{0}, which equals 1), - 4 is in the position of tens (10
^{1}) - 3 is in the position of hundreds (10
^{2}) - 2 is in the position of thousands (10
^{3}) - Meanwhile, the digit 6 after the decimal point is in the tenths (1/10, which is 10
^{-1}) and 7 is in the hundredths (1/100, which is 10^{-2}) position - Thus, the number 2345.67 can also be represented as follows: (2 * 10
^{3}) + (3 * 10^{2}) + (4 * 10^{1}) + (5 * 10^{0}) + (6 * 10^{-1}) + (7 * 10^{-2})

### How to Read a Binary Number

In order to convert binary to decimal, basic knowledge on how to read a binary number might help.

As mentioned above, in the positional system of binary, each bit (binary digit) is a power of 2. This means that every binary number could be represented as powers of 2, with the rightmost one being in the position of 2^{0}.

**Example**: The binary number (1010)_{2} can also be written as follows: (1 * 2^{3}) + (0 * 2^{2}) + (1 * 2^{1}) + (0 * 2^{0})

### How to Convert Binary to Decimal

There are two methods to apply a binary to decimal conversion.

The first one uses positional representation of the binary, which is described above. The second method is called double dabble and is used for converting longer binary strings faster.

## AS SEEN ON.

It doesn’t use the positions.

### Method 1: Using Positions

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

**Step 2**: Starting with the least significant digit (LSB - the rightmost one), multiply the digit by the value of the position. Continue doing this until you reach the most significant digit (MSB - the leftmost one).

**Step 3**: Add the results and you will get the decimal equivalent of the given binary number.

Now, let's apply these steps to, for example, the binary number above, which is (1010)_{2}

**Step 1**: Write down (1010)_{2}and determine the positions, namely the powers of 2 that the digit belongs to.**Step 2**: Represent the number in terms of its positions.(1 * 2

^{3}) + (0 * 2^{2}) + (1 * 2^{1}) + (0 * 2^{0})**Step 3**: (1 * 8) + (0 * 4) + (1 * 2) + (0 * 1) = 8 + 0 + 2 + 0 = 10- Therefore, (1010)
_{2}= (10)_{10}

*(Note that the digits 0 in the binary produced zero values in the decimal as well.)*

### Method 2: Double Dabble

Also called doubling, this method is actually an algorithm that can be applied to convert from any given base to decimal.

Double dabble helps converting longer binary strings in your head and the only thing to remember is ‘double the total and add the next digit’.

- Step 1: Write down the binary number. Starting from the left, you will be doubling the previous total and adding the current digit.
In the first step the previous total is always 0 because you are just starting. Therefore, double the total (0 * 2 = 0) 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. Repeat this until you run out of digits.
- Step 4: The result you get after adding the last digit to the previous doubled total is the decimal equivalent.

Now, let’s apply the double dabble method to same the binary number, (1010)_{2}

- Your previous total 0.
## Related Calculators:

Your leftmost digit is 1. Double the total and add the leftmost digit

(0 * 2) + 1 = 1 - Step 2: Double the previous total and add the next leftmost digit.

(1 * 2) + 0 = 2 - Step 3: Double the previous total and add the next leftmost digit.

(2 * 2) + 1 = 5 - Step 4: Double the previous total and add the next leftmost digit.

(5 * 2) + 0 = 10

This is where you run out of digits in this example.

Therefore, (1010)_{2} = (10)_{10}

#### Binary to decimal conversion examples

**Example 1**: (1110010)_{2} = (114)_{10}

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 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

**Example 2**: (11011)_{2} = (27)_{10}

Method 1:

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

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

= 1 + 2 + 0 + 8 + 16 = 27

Method 2:

(0 * 2) + 1 = 1

(1 * 2) + 1 = 3

(3 * 2) + 0 = 6

(6 * 2) + 1 = 13

(13 * 2) + 1 = 27

Related converters:

Decimal To Binary Converter

#### Binary Decimal Conversion Chart Table

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 |