# Binary system

The **binary system** is a way of representing numbers in base 2, i.e. using only the digits 0 and 1. The term 'Binary' means *composed of two parts* and comes from the Latin, originally meaning "two by two".

A number written in the system can be denoted by following it with a subscipt 2, i.e. _{2}. Each digit represents the number of a power of 2 in the complete number, similarly to in the decimal system, where each digit represents the number of a power of 10. The power is defined by the number of digits in the number from right to left through the digit, minus 1, e.g. 100_{2}, where the digit 1 is the third digit from the right, and thus represents 2^{2}, or 4. While it is generally impractical for human use, it is the mainstay of modern computing. A binary system is also used in electronics, which commonly uses **0** to mean "no voltage is present" **1** to mean "a voltage is present". Binary notation is used in circumstances in which a thing is in one of two possible conditions and no other condition is possible; the switch is on or the switch is off, the page has data on it or the page has no data.

To increment a binary number, follow this rule:

- Current digit is the end digit
- Change the current digit
- If current digit = 1
- Then:
- Shift current digit to away from the end digit
- Go to step 2

- Else:
- You're done.

- Then:

The first 16 binary digits:

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

0 | 0 | |

1 | 1 | |

2 | 10 | |

3 | 11 | |

4 | 100 | |

5 | 101 | |

6 | 110 | |

7 | 111 | |

8 | 1000 | |

9 | 1001 | |

10 | 1010 | |

11 | 1011 | |

12 | 1100 | |

13 | 1101 | |

14 | 1110 | |

15 | 1111 | |

16 | 10000 |