2012-01-11 19:31

You know more math than you think: non-decimal numbers

Yes, you do. If you are a frequent reader of this blog, then you probably already know about binary numbers, hexadecimal numbers, and sundry non-decimal numbers. You know, the kind we nerds know about. The ones that make us confuse thanksgiving and christmas because oct(31) == dec(25).

But how about normal people (or as I like to call them: people)? Well, they may look at you confusedly if you tell them that they use way more exotic things every day.

Let's start with the time. When you say "it's 10:30? well, that's a base-60 number.

If we add days, it gets harder, because days are base-24. So "2 days, 10 hours and 30 minutes" is just a difficult way to say 2*24*60 + 10*60 +30 minutes. It's a numerical system with two different bases.

Sure, it doesn't do the cutesy thing hex does of having extra symbols, like A meaning 10, but it's exactly that, except 20 is written "20" or "8PM".

And how about January 11th, at 5:20 PM? Well, that is also another way to express a number of minutes, in an even more complicated mixed-base system!

January = 0 months = 0 days = 0 hours = 0 minutes
11th = 11 days = 251 hours = 15060 minutes
5PM  = 17 hours = 1020 minutes
20 = 20 minutes

Total: 16100 minutes

That way to express a date uses a mix of base 60, base 24, and base 365 (if we can, please, ignore leap years) or maybe base 60, base 24, base ~30 and base 12

I don't know if numerical systems with non-fixed bases have a name in mathematics, yet you use them, random non-math-person!

And you can even do arithmetic on them! Yes, you! You know what exact time it will be at "Jan 9th 2:10 + 12:15". You can even do multi-base arithmetic in your head.

And I have not mentioned seconds (base 60 again), years (multiple base 10 digits) and second fractions.

Yet, when hex and binary are explained to people in school, it's incredibly hard to make them "get it". And once they get that if you try to explain, say base-3 numbers, it's confusing again.


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