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Base 20 is the number system for describing quantities. It is used everyday in many languages of Mesoamerica.

Base 20 can be used to describe any number (like base 10), z, member of the the natural set (...-2, -1, 0, 1, 2):

z = a*20^0 + b*20^1 + c*20^2 ....

z = a*1 + b*20 + c*400 ...

An easy way to remember the multiplying factor is to think of it in terms of ten times two to the n:

20^n = 10*2^n for all n >= 1

Once we have the power of two, it is substancially simpler, since the power of two series is quite common in computer programming:

{ 2, 4, 8, 16, 32, 64, 128, 256, 512... }

To find the correct multipliers for each factor, if starting from another base (like base 10), you divide by the closest, smaller than or equal to factor. Then you take the remainder and repeat. When you reach any number less than 20, you finished.

Example:

2000b10 / 400 = 5 + 0

The main issue in representing numbers in base 20 is the lack of glyphs to represent 11b10 throught 20b10. You can use normal numbers from 0-9, then add nine letters, but it's not very amusing to that. What you can do is use an approximation of the old Mesoamerican system. To do this, we can represent zero as just a 0. One is a ".", two is ":", three is ".:" and four is "::". five is a bar, "|". six is "|." ten "||". nineteen would be "|||::". twenty is .0b20 . To make 2000b10 then is:

2000 = |00

2001 = |0.

A larger number, like 15,321b10 is then:

15,321/8,000= 1 + 7,321/400=18 + 121/20=6 + 1

15,321 = .|||.:. This system is only efficient for certain things. Data-wise it is inefficient when compared to base 10.

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