**Binary Number System
**

Computers use binary digits. And some puzzles can be solved using binary numbers.

A Binary Number is made up of only 0s and 1s.

110100 Example of a Binary Number

There is no 2,3,4,5,6,7,8 or 9 in Binary!

How do we Count using Binary?

Binary | |

0 | We start at 0 |

1 | Then 1 |

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

**Decimal **

Well how do we count in Decimal?

0 | Start at 0 |

... | Count 1,2,3,4,5,6,7,8, and then... |

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 |
||

0 | 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 ... ? |

Decimal What happens in Decimal ... ?

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 0 Start at 0 • 1 Then 1 •• 10 Start back at 0 again, but add 1 on the left

Binary |
||

0 | Start at 0 | |

• | 1 | Then 1 |

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

••• | 11 | |

•••• | 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 |

••••••••• | 1001 | And so on! |

Binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). He base-2 system is a positional notation with a radix of 2.

Binary 8-bits word length: |
|||||||

2^{7} |
2^{6} |
2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |

= 128 | = 64 | = 32 | = 16 | = 8 | = 4 | = 2 | = 1 |

Decimal vs Binary

Here are some equivalent values:

Decimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

Binary 4-bits word length: |
0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |

we start counting from the right

1 | 2 | 3 = 1 + 2 | 4 | 5 = 4 + 1 | 6 = 4 + 2 | 7 = 4 + 2 + 1 | 8 |

2^{0} |
2^{1} |
2^{1} + 2^{0} |
2^{2} |
2^{2} + 2^{0} |
2^{2} + 2^{1} |
2^{2} + 2^{1} + 2^{0} |
2^{3} |

0001 |
0010 |
0011 |
0100 | 0101 | 0110 | 0111 | 1000 |

Recherche personnalisée