To convert a decimal (base 10) number to any other base, we simply repeatedly divide by the base until we have a quotient of zero. Specifically, the dividend starts with the number that we want to convert, the divisor will always be the base. The remainder of each successive operation indicates the digit in the new base first at the right-most position and then moving left. The quotient of each step becomes the dividend of the subsequent step.

Let’s first try converting the number 28_{10} to octal (base 8):

The dividend is the decimal number that we want to convert, in this case 28. The divisor is the base to which we want to convert, in this case 8. The remainder indicates each successive digit. We stop the process when the quotient is 0.

Step | Dividend | Divisor | Quotient | Remainder |
---|---|---|---|---|

1 | 28 | 8 | 3 | 4 |

2 | 3 | 8 | 0 | 3 |

So, 28_{10} is 34_{8}. (Remember that we read the remainder from bottom to top.)

Let’s try converting the number 567_{10} to octal:

Step | Dividend | Divisor | Quotient | Remainder |
---|---|---|---|---|

1 | 567 | 8 | 70 | 7 |

2 | 70 | 8 | 8 | 6 |

3 | 8 | 8 | 1 | 0 |

4 | 1 | 8 | 0 | 1 |

So, 567_{10} is 1067_{8}.

Let’s try converting the number 63,215_{10} to hexadecimal:

Step | Dividend | Divisor | Quotient | Remainder |
---|---|---|---|---|

1 | 63215 | 16 | 3950 | 15 |

2 | 3950 | 16 | 246 | 14 |

3 | 246 | 16 | 15 | 6 |

4 | 15 | 16 | 0 | 15 |

So, 63,215_{10} is hexadecimal [15][6][14][15], or more conventionally, F6EF_{16}.

(Remembering that in hexadecimal, we use the digit “F” for 15, “E” for 14, etc.)

Finally, let’s convert the number 53410 to binary:

Step | Dividend | Divisor | Quotient | Remainder |
---|---|---|---|---|

1 | 534 | 2 | 267 | 0 |

2 | 267 | 2 | 133 | 1 |

3 | 133 | 2 | 66 | 1 |

4 | 66 | 2 | 33 | 0 |

5 | 33 | 2 | 16 | 1 |

6 | 16 | 2 | 8 | 0 |

7 | 8 | 2 | 4 | 0 |

8 | 4 | 2 | 2 | 0 |

9 | 2 | 2 | 1 | 0 |

10 | 1 | 2 | 0 | 1 |

So, 534_{10} is 10 0001 0110_{2}