7 | x | 10^{2} | =700 |

8 | x | 10^{1} | = 80 |

3 | x | 10^{0} | = 3 |

783_{10} | Total | = 783_{10} |

In the decimal system, we are counting how many 10s, 100s, 1000s, 10000s etc. there are. Then we are multiplying the number depending on where it is positioned, and finally, we add them up.

If we were to do the same to the 8th base, then the above table will look as follows:

1 | x | 8^{3} | =512 |

4 | x | 8^{2} | =216 |

6 | x | 8^{1} | =48 |

7 | x | 8^{0} | =7 |

1467_{8} | Total | = 783_{10} |

Now the number 783

_{10}~= 1467

_{8}. This means that any number (like 783) can be written to any number base; even its own. So in computers we are interested in binary digits, as the switches in circuits are either ON or OFF. With this in mind, the number above (783) would be written in binary form as follows:

1 | x | 2^{9} | =512 | |

1 | x | 2^{8} | =256 | |

0 | x | 2^{7} | =0 | |

0 | x | 2^{6} | =0 | |

0 | x | 2^{5} | =0 | |

0 | x | 2^{4} | =0 | |

1 | x | 2^{3} | =8 | |

1 | x | 2^{2} | =4 | |

1 | x | 2^{1} | =2 | |

1 | x | 2^{0} | =1 | |

1100001111_{2} | Total | = 783_{10} |

This means that:

1100001111

_{2}~=783

_{10}

Here is a sequence that may simplify this process a bit better:

2

^{0}= 1 = 1

_{2}

2

^{1}= 2 = 10

_{2}

2

^{2}= 4 = 100

_{2}

2

^{3}= 8 = 1000

_{2}

2

^{4}= 16 = 10000

_{2}

2

^{5}= 32 = 100000

_{2}

2

^{6}= 64 = 1000000

_{2}

2

^{4}= 128 = 10000000

_{2}

and so on...

So now, gifting somebody $32.00 in decimal form will be written in binary as $100,000

_{2}and giving $64.00 = $1,000,000

_{2}which is a LOT OF MONEY... :).

As the joke goes: There are 10 kinds of people, the kind that understand binary numbers and those who do not.