# Decimal to Binary Converter

To use this **decimal to binary converter** tool, you should type a decimal value like 308 into the left field below,
and then hit the Convert button.
This way you can convert up to 19 *decimal* characters (max. value of 9223372036854775807) to *binary* value.

### Decimal to binary conversion result in base numbers

## 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 Hinduâ€“Arabic numeral system. 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}) + (6 * 10^{-1}) + (7 * 10^{-2})

## 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. This is the most efficient system to detect an electric signalâ€™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.

### 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})

#### Decimal to binary conversion examples

- (51)
_{10}= (110011)_{2} - (217)
_{10}= (11011001)_{2} - (8023)
_{10}= (1111101010111)_{2}

Related converters: Binary To Decimal Converter

#### Decimal Binary Conversion Chart Table

Decimal | Binary |
---|---|

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

11 | 1011 |

12 | 1100 |

13 | 1101 |

14 | 1110 |

15 | 1111 |