The Dozenal System: Part One-The Base of a Number System

Duodecimal Digits (c) Erik Engheim, CC BY-SA 4.0

When I was a kid, first learning how to count, the most natural and obvious method, as well as the one taught is to use your fingers, of which most humans have 10. Once you master the ability to count beyond 9, you run into an issue, you are out of fingers. At this point, you close your hands, and begin to count to ten again, remembering how many times you have already done so. This is exactly how counting functions in our normal life. This number system is called base 10, as there are 10 digits we use: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. A closer examination of the “closing your hands and starting over” gives insight into how a number’s base actually works.

After a digit goes past the base value of a system, for normal (decimal) it is 10, you take the place in front of the digit and increase its value by one. This means that the digit in front of it has a value the base value times larger. For the decimal system, in the number 241, the 2 really means 2*102, the 4 means 4*101and the 1 means 1*100.

I went for a long period of my life thinking decimal is the only way to count until I began computer programming.

Computers function in a different way of counting, called binary, or base 2. This is easier for information transfer, as the two digits, 0 and 1, can easily be communicated with strong and weak electric pulses. With so few digits before the base value is passed, binary numbers often end up being very long, and difficult to understand at a glance, like 241, written as 11110001. As a solution to this, computer scientists also use two other systems, octal and hexadecimal. Octal has a base value of 8, with the 8 digits 0, 1, 2, 3, 4, 5, 6 and 7 and hexadecimal has a base value of 16 with the sixteen digits 0, 1, 2, 3, 4, 5, 6 ,7, 8 ,9, a, b, c ,d, e and f. These make writing numbers shorter than binary, and more comprehensible, for example, 241 is written 361 in octal and f1 in hexadecimal.

Other examples of different base systems include minutes (60 seconds in a minute), feet (12 inches in a foot), scores (20 years in a score), weeks (7 days in a week) and even dozens (12 items in a dozen). With all of these different counting systems, it begs the question why do we still use 10?

The only reason we use 10 is simply that we have 10 fingers. But, if we abandon that reason, are there other base systems that are objectively better? I am not the only one to ask this question, and the answer decided has been 12, for the so-called dozenal system. In the next part of this blog series, I will talk about why the dozenal system is better, the characters used for 11 and 12 and the time we almost ended up using it.

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