In the 1982 movie E.T. the Extra-Terrestrial, we meet an alien who has been left stranded on earth when his fellow scientists, spooked by approaching humans, make a hasty retreat in their spaceship.

E.T. appears to have four fingers on each hand.

Let us journey through a thought experiment: Suppose the inhabitants of E.T.’s planet have developed a place value number system that, like our own decimal (base 10) system, works by grouping by the total number of fingers they have. So instead of ones, tens, hundreds (ten tens), thousands (ten hundreds), etc. the places in the E.T. number system are ones, eights, sixty fours (eight eights), five hundred twelves (eight sixty fours).

How would you write the decimal numbers one through one hundred in base 8? How would you write larger base 10 numbers, like one thousand or one million?

Think about how our decimal number system works to the right of the decimal point. Consider what it means to say, for example, 3.4987. How do we know what the place values represent? What does the 8 represent in this number?

If I wrote the number 123.45 in base 8, what base 10 number would that be?

Could you develop an algorithm to add or subtract in base 8?