Subject:

## Converting from decimal to binary - Applying mathematical reasoning - Pre-Algebra - Khan Academy

## 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.

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### 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 Hindu–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}) + (5 * 10^{0}) + (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 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 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 |