# Binary Notation

## Introduction

**Binary notation** is another base to represent numbers, like Hexadecimal Notation.

## Representation

Binary only has two digits, 0 and 1. Each position is a power of two. 101101 = 1*1 + 0*2 + 1*4 + 1*8 + 0*16 + 1*32 = 45 in base 10

It is also the base computers use because of the fact that it can be represented as on or off - Digitally. However, it is difficult for humans to decode long strings of 1's and 0's, so it is often represented in Hexadeciaml (or Hex for short) as this is a lot shorter and is easy to convert between binary and hex. You just take each nibble and convert it indvidually. With practice you can be very quick doing this:

### Conversion

Binary | Hex | Base 10 |
---|---|---|

0000 | 0 | 0 |

0001 | 1 | 1 |

0010 | 2 | 2 |

0011 | 3 | 3 |

0100 | 4 | 4 |

0101 | 5 | 5 |

0110 | 6 | 6 |

0111 | 7 | 7 |

1000 | 8 | 8 |

1001 | 9 | 9 |

1010 | A | 10 |

1011 | B | 11 |

1100 | C | 12 |

1101 | D | 13 |

1110 | E | 14 |

1111 | F | 15 |