Tool to make binary conversions. Binary code is a numeric system using base 2 used in informatics, symbols used in binary notation are generally zero and one (0 and 1).

Binary Code - dCode

Tag(s) : Arithmetics, Character Encoding, Substitution Cipher

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The binary is often used to encode text in ASCII, use the dedicated page to translate binary into text:

⮞ Go to: ASCII Code

Tool to make binary conversions. Binary code is a numeric system using base 2 used in informatics, symbols used in binary notation are generally zero and one (0 and 1).

To convert a number $ N $ to binary (format with zeroes and ones) consists in an arithmetic base conversion from base 10 (decimal base noted $ N_{10} $) to base 2 (natural **binary code** noted $ N_{2} $).

__Example:__ $ 5_{10} = 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 101_{2} $

The method consists in making successive divisions by $ 2 $ and noting the remainder ($ 0 $ or $ 1 $) in the reverse order.

__Example:__ With the number 6: $ 6/2 = 3 $ remains $ 0 $, then $ 3/2 = 1 $ remains $ 1 $, then $ 1/2 = 0 $ remains $ 1 $. The successive remainders are $ 0,1,1 $ so $ 6_{10} $ is written $ 110_{2} $ **in binary**.

Associate with each letter of the alphabet a number, for example by using the A1Z26 code or the ASCII code. This will replace each letter by a number that can then be converted to binary (see above).

__Example:__ AZ is 65,90 (ASCII code) so 1000001,1011010 **in binary**

Similarly for binary to text translation, convert the binary to a number and then associate that number with a letter in the desired code.

It is a base conversion from base 2 to base 10

__Example:__ 111 (base 2) = 1*2^2+1*2^1+1*2^0 = 7 (base 10)

A bit (contraction of binary digit) is a symbol in the binary notation: 0 or 1.

In computer informatics, size is limited, numbers are stocked in memory cells of size N where N is the number of bits.

This depends on the size of the number, here are the min-max intervals:

0-1 | 1 |

2-3 | 2 |

4-7 | 3 |

8-15 | 4 |

16-31 | 5 |

32-63 | 6 |

64-127 | 7 |

128-255 | 8 |

256-511 | 9 |

512-1023 | 10 |

1024-2047 | 11 |

2048-4095 | 12 |

2^(n-1) - (2^n)-1 | n |

In informatics, one's complement is writing a number negatively inversing 0 and 1.

__Example:__ 0111 becomes 1000, so 7 becomes -7

In informatics, one's complement is writing a number negatively inversing 0 and 1 and adding 1.

__Example:__ 0111 becomes 1001

There are 10 kinds of people in the world, those that understand binary, and those that don't...

10 **in binary** equals 2 in decimal.

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Please, check our community Discord for help requests!

- Binary to Numbers Converter
- Binary to Text (ASCII) Converter
- Binary Converter/Encoder
- How to convert a number in binary?
- How to convert a text in binary?
- How to convert from binary
- How to translate binary
- What is a bit?
- Why defining a number of bits?
- how many bits are necessary to represent a number?
- What is 1's complement?
- What is 2's complement?
- Why is there 10 kinds of people in the world?

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