Binary numbers --- Introduction --- Addition --- Multiplication --- Counter --- Card game

When we count using decimal or base 10, our normal counting system, we count up to nine using a different symbol each time: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Then for ten, we use two digits: 10. Beyond that, we combine the same ten symbols in various ways to give all possible numbers. This is called a positional system. So 3528 means three thousand, five hundred and twenty eight, or 3000 + 500 + 20 + 8. But you can count using less digits than this. You must have a zero. But you're not going to get anywhere with just zero! So you need a digit for one as well. This is called binary or base 2.Enter a number in either box, and click on the button. Remember that binary numbers must only have ones and zeroes.

Number | Decimal | Binary | Comments |
---|---|---|---|

zero | 0 | 0 | Binary same as decimal |

one | 1 | 1 | Binary same as decimal |

two | 2 | 10 | Binary has run out of symbols, so needs two |

three | 3 | 11 | 10 (2) + 1 |

four | 4 | 100 | Binary run out of symbols again, three needed |

five | 5 | 101 | 100 (4) + 1 (no 10's) |

six | 6 | 110 | 100 (4) + 10 (2) (no 1's) |

seven | 7 | 111 | 100 (4) + 10 (2) + 1 |

eight | 8 | 1000 | Binary run out of symbols again, four needed |

© Jo Edkins 2006 - Return to Numbers index