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The digits in the dozenal numeral system

Teaching Kids About Alternative Number Bases

We learn to count to 10 on our fingers as kids. The 10 based system becomes so ingrained in our way of thinking about numbers that it becomes synonymous with numbers. This 10 based system, is called the decimal number system or Arabic number system. We become so accustomed to decimal numbers that we think that numbers and decimal numbers are one and the same thing.

Dozenal or Duodecimal Numeral System

There are many alternatives to the decimal number system. You may already have heard about the binary number system used by computers. One of my favorites is the dozenal number system. Dozenal means the base is 12 rather than 10. I’ve written an earlier article about what makes this number system so interesting.

  • There are 12 inches in a foot.
  • Eggs are sometimes packed in dozens (12).
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2 dogs + 2 legs = 22₄ = 2×4 + 2 = 10₁₀

Octal Numeral System

We could continue the experiment with other animals such as octopus,

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1 octupus + 2 tentacles = 12₈ = 1×8 + 2 = 10₁₀
0 1 2 3 4 5 6 7
74₁₀ = 7 × 10¹ + 4 × 10⁰ 
= 7 × 10 + 4 × 1
= 70 + 4
112₈ = 1×8² + 1×8¹ + 2×8⁰ 
= 1×64 + 1×8 + 2×1
= 64 + 8 + 2 = 74₁₀
5 feet + 11₁₀ inches = 5'11'' = 5×12₁₀ + 11₁₀ = 71₁₀
5 feet + E inches =  5×10₁₀ inches + E inches = 5E inches

Dozenal Counting

While base twelve numbers might be practical in a lot of ways, you’d probably object that it is highly impractical to work with as you can’t count to twelve on your fingers easily. Or can you?

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Advantages of Dozenal Numbers over Decimal Numbers when Multiplying

Base twelve is actually a lot easier to learn the multiplication table for. Consider the decimal multiplication table. You will notice there are a lot of irregular number sequences.

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Recap

The idea here is really just about learning to think about numbers. Even though you don’t really need to know about octal or dozenal numbers it helps your general number understanding, knowing about them. If you have to work with numbers which are dozenal in nature such as time, feet and inches then using the dozenal system would make it easier to perform calculations on them.

Geek dad, living in Oslo, Norway with passion for UX, Julia programming, science, teaching, reading and writing.

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