Geek'd

Yesterday my wife and I inflicted some geekishness on our daughter, and we got away with it.

She had made a joke about my wife's age, and I said well, kiddo, that IS her age -- but, you know, in hex. She seemed puzzled, so I said 'hex is base sixteen numbering. Have you ever heard of bases for numbers?' She had not, so I said well, in the number 10, what does the zero mean? And she said 'that there's nothing there'. So I said Okay, what does the one mean? And she thought a minute, and said 'it means theres one in that position.' One what? I asked. 'One -- one ten, ' she said, not too sure. "Right,", I replied. The numbering system you're using is base ten. The first position in any numbering system is always how many ones do you have, and the second is how many bases you have. So in base ten, a one in that position means you have one ten. What would a two mean?' 'Two tens', she replied. 'And suppose this was base sixteen -- what would a one in that position mean?' 'It would mean sixteen, ' she said. "And what about a one in that position, with a one in the ones position?' She thought a minute. 'Sixteen plus one. Seventeen'. So, my wife said, a seventeen -- one seven -- in base ten is the same as a ten -- one zero -- in base sixteen.' We both looked at my daughter, who was nodding slowly. 'I get it', she said, after a minute. 'So if you had two zero in base sixteen, thats two sixteens and no ones, or 32 in base ten'.

We smiled.