# Binary Numbers

## Introduction

```
A Binary Number is made up of only 0s and 1s.
Example: 110111
There is no 2, 3, 4, 5, 6, 7, 8 or 9 in Binary!
```

### How do we Count using Binary?

It is just like counting in decimal except we reach 10 much sooner.

Binary | Explanation |
---|---|

0 | We start at 0 |

1 | Then 1 |

??? | But then there is no symbol for 2 … what do we do? |

#### Well how do we count in Decimal?

Decimal | Explanation |
---|---|

0 | We start at 0 |

1 | Then 1 |

2-8 | Count 1,2,3,4,5,6,7,8 |

9 | This is the last digit in Decimal |

10 |
So we start back at 0 again, but add 1 on the left |

#### The same thing is done in binary ...

Binary | Explanation |
---|---|

0 | We start at 0 |

1 | Then 1 |

10 |
Now start back at 0 again, but add 1 on the left |

11 | 1 more |

??? | But NOW what … ? |

#### What happens in Decimal?

Decimal | Explanation |
---|---|

99 | When we run out of digits, we … |

100 | … start back at 0 again, but add 1 on the left |

#### And that is what we do in binary ...

Binary | Explanation |
---|---|

0 | We start at 0 |

1 | Then 1 |

10 |
Now start back at 0 again, but add 1 on the left |

11 | 1 more |

100 |
start back at 0 again, and add one to the number on the left but that number is already at 1 so it also goes back to 0 and 1 is added to the next position on the left |

101 | |

110 | |

111 | |

1000 |
Start back at 0 again (for all 3 digits), add 1 on the left |

### See how it is done in this little demonstration

128

0

64

0

32

0

16

0

8

0

4

0

2

0

1

0

= 0