Counting with Aliens?

Here's a little tale to introduce different number systems for your budding little mathematician. Your little one may only be familiar with the decimal numeral system, or Base 10. This brief story introduces the octal & hexadecimal numeral systems.

One fine, sunny day in the not too distant future, an ambassador from Earth was at a summit with an ambassador from Planet Hexadecimal and an ambassador from Planet Octal. During this friendly summit, they decided to do some counting on their fingers. In unison, they started "1, 2, 3, 4, 5, 6, 7, ..." and when they got to "8", the ambassador from Planet Octal counts on his very last finger of his hands, and he won't be able to count further than that using just his fingers. You see, people from Planet Octal have only 8 fingers to count with. In their number system, which is the octal numeral system (Base 8), when they want to represent 8 "things", such as fingers, they represent it with "10". The digit in the tens column tells us how many "full hands" of stuff we have. In the case of Planet Octal, two full hands has eight fingers.

Since the ambassador from Planet Octal ran out of fingers at "8" (his "10"), the other two continued to count "9, ..." and at that point, the ambassador from Earth was upon his very last finger, what Earthlings call "10". But the ambassador from Planet Hexadecimal could still keep going, so he did and counted "11, 12, 13, 14, 15, ... and finally, 16!" The ambassador from Planet Hexadecimal could continue to count many more numbers on his hands than the other ambassadors because people from his planet have 16 fingers! Because they have more fingers on their hands, math on their planet uses the hexadecimal numeral system (Base 16). When people from Planet Hexadecimal WRITE "10", the NUMBER they represent is still two whole full hands worth, though in their case that's 16 fingers.

An important lesson in all this alien finger counting is this: the actual NUMBER of things don't change between numerical bases, just how they are WRITTEN.

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