This is the digital age. Information is represented with the simplest of logic choices. It is either on or off, up or down, yes or no, true or false, right or left, etc. Those simple logical options are combined into more complicated logical arrangements in order to yield more complex outcomes. The basic unit of logic is dependent only upon having two digits to represent it, the zero and the one.

Modern day computer and digital technology processes the 0 or 1 bits of data at incredible rates. My Apple Mini cruises along crunching those digits at a rate of 2.5 billion per second. That isn’t top of the line. But, it gets my jobs done fast enough.

Today, I want to see if you learned how to represent numbers with these two digits. Were you paying attention in school a long time ago? Here is a table of two columns. The left column has some numbers in the base 10 system. The right column has numbers representing them, but in the base 2 system. Notice the pattern. Certain values stand out such as 1, 2, 4, and 8. What about 16?

*See if you can fill in the missing values without resorting to Google*.

Base10 | Base2 |
---|---|

0 | 0 |

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

100000 | |

63 | 111111 |

256 | |

500 | 111110100 |

1024 | |

2014 | |

32768 |

When I was in my early tens I was browsing through a paperback collection of articles from the old Ripley’s Believe It or Not newspaper column. One headline that caught my attention asserted that Babe Ruth hit 111100 home runs in one season, which is true in base two.

That’s funny.