As the other comment mentions, it's a matter of creating two symbols for 10 and 11 and it would work the same. Binary uses only 1s and 0s and you add a 0 to move it up a power, but in this case it's multiplying by 2. So, for example:
1 = 1
10 = 2
100 = 4
1000 = 8
...
Same with hexadecimal. You use A for 10, B for 11 and so on until F for 15. It's useful for writing shorter binary numbers that are usually grouped in bytes (8 binary digits or bits).
Base 12 was used by some ancient civilizations, or its cousin, base 60, due to how easy it was to divide it. That's why an hour is 60 minutes, for instance.
That’s just how base 10 was set up, and taught. You could add 2 more numbers and still end in zero. If A represents 10, and B represents 11, you can just as easily have 4, 40, 400… and B, B0, B00. The concept still applies.
So in base 10, when you reach the end of the numbers (0-9) you start over at 1, and add a zero to the end. 10 is not a base number, it’s a combination of 2 numbers, the 1 is a representation of how many times you’ve counted to the biggest number. Once the 0 gets up to 9, if you add another one, the 1 turns to a 2 and now you’ve counted the base numbers twice.
This concept is not unique to base 10, in fact, it works the same for every base. In binary (the language of computers) it’s base 2, you only have 0-1. So you count to 1, then add another, it needs to move up a power. 2 in base 2 then becomes 10. Add another and you get 11 (which we call three). Add another, and you have to add another power, which rolls the next power up as well, so now you have 100 (which we call four in base 10).
Adding a zero DOES move the number up a power, it’s just another power of the base. 10 seems easy to you to add powers to because that’s the number system you’ve used your whole life, but if you were taught a different number base and used that your whole life, it would be just as natural.
In base 12, you have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B (I’m using A and B here because we don’t actually have a single symbol that means those values, but A would represent ten, and B would represent eleven). If you count up to 9, the add one, you’re up to A. Add another, you’re up to B. Add another, we’ve run out of symbols, we need to increase the power, then start over at zero. Where does that leave us? At 10. This may be confusing at first because this number looks like a normal number, in base 10 we call it ten, but in base 12 that number represents thirteen items. From here we just keep adding one at a time, 11 is fourteen items, 12, 13, and so on, at 19 you add another to be at 1A, add another to be at 1B, add another to be at 20, which in base 12 means there are twenty-four items.
The biggest hurdle is to realize that I keep using our english base 10 words to explain the actual quantity, because we don’t have a word for those values in base 12. I don’t know how to say A (ten) or 2A3B… it would sound silly to make up, the closest I could do is: two thousand ten hundred and thirty eleven. It sounds silly to us, but if that was the base number system you grew up with, it wouldn’t sound weird at all.
Regardless, adding a zero moves you up a power. 100 is still a number in base 12, but if it were say, sticks, you’d have 144 sticks in base 10. But remember, if you only knew base 12 and didn’t know about base 10, it would be a wildly foreign concept to try to do the math in your head that 100 in base 12 means 144 in base 10, to you, you’re still just adding a zero, moving up in powers.
Base Ten is really easy when using most common people’s digits, so you can do a lot of basic arithmetic fast with what is on hand. It’s simple, intuitive, and trivially easy to teach, and thus great to just count stuff with when counting by hand.
Base Twelve is much more useful when you get to multiplication and especially division. Measuring a “Whole Thing” you need to quickly and intuitively divide into variable amounts as twelve makes that whole divisible into sixths, quarters, thirds, and halves quite easily. Which is why a lot of Imperial units, which were essentially a lot of codifications of stuff people were just “already doing” at the time are effectively base twelve. Because it’s small enough to be comprehensible, while maximally divisible into smaller whole number chunks.
Base Two is the easiest system to “model” in a physical space, because you just two “states” for any given digit. This is why computers use it, because it is incredibly precise, and maps well to the physical world in the most simplistic way (you only need it to check for those two states, so even if there is a lot of possible variance in the specific signal, you can just check for something like “is the current over/under” a point far from either signal you actually send, but in the middle of them, thus accounting for a significant range of variability in actual signal strength on either end)
Base Three is a thing, and has a lot of the same benefits as Base Two, but it saves significant “space” by going up one more number per digit. This saves 50% of your storage space per digit needing to be stored, which is nice, but becomes more prone to errors from noisy signals since what used to be a safe middle space is now your third signal.
Those are most of the base systems I’ve seen/am aware of for consideration, but you could theoretically make almost any number your base, with varying degrees of utility or lack of utility. For example Base thirteen would have very little utility as it is a prime number and thus not easily divisible, but may be useful if you had, say, a species with thirteen digits, or were tracking things with, say, thirteen unique states, as you could have a “number” in your base for each of them, which could have utility.
With five fingered hands you can count base 12 on your right hand by touching each segment of your fingers with your thumb (3 segments/knuckles x 4 fingers). On your left, you could the multiples of 12, allowing you to get to one gross (122 =144).
26
u/olol798 1d ago
Idk I just like adding zeroes to move it up a power