number systems
Talking Basically About Bases
You may or may not know that we operate in a base-10 number system, which is a beautiful thing. It spares us from the agony of Roman numerals, where years looked something like this:
Instead of like this:
Remember all that talk about place value in elementary school? Ones, tens, hundreds, thousands, and so on? That’s the base-10 idea. Multiply 10 by itself successively, and you get the next place value.
Ten isn’t the only number to base a system on, though. Convenient with our ten-fingered anatomy, but it’s not even the only base we use on a regular basis. Time notoriously operates on non-ten bases. (Makes figuring elapsed time tricky for some students.) And since this particular country refuses to go metric, most of our measurements avoid the ease of base-10.
There are plenty of practical applications for other bases, but when I first learned about them in school, I remember just thinking it was cool to write a number that meant something other than what it looked like. Sort of a mathematical code.
For example, take base-8. We have to reassign all the place values. The ones place is still the ones place. The next place to the left is now the eights place. And the next is the eight-squareds (or sixty-fours) place, followed by the eight-cubeds (or five-hundred-twelves) place. So earlier I mentioned the year 1988. In base-8, that’d be
3 five-hundred-twelves
7 sixty-fours
0 eights
4 ones
So the year 1988 converts to 3704.
If someone gave me a worksheet of numbers to convert to different bases right now, I’d probably be a happy camper working through it.
And that concludes our Yes-I-Am-A-Geek moment for this week.