memes

Wouldn't that be base 1?

8 rocks would be 二四 in base 4

ok but what about 16? there's symbols for powers of 10 but not for powers of 4

Having seen this for the first time, that was my first thought for an improved punchline.

Yes this is the better version that I've seen too

When you count up the 1's place, you go 0,1,2,3,4,5,6,7,8,9 and then it rolls over into the 10s place.

But in "base 4", it goes: 0,1,2,3,10,11,12,13,20. 3 is the highest value possible in any of the digits place.

Therefore "10" in base 4 = 4 in base 10, but saying it in base 4 is written as 10.

You can change your base to any base and whatever base it is would have to be written as base 10 because the number above the highest one in that base doesnt exist, it's 10.

Lots of good explanations here, but one thing I'd like to clarify. WHY we add digits together to represent larger numbers. Understanding this helped me to count in binary when I was a young IT technician.

In base 10, we have 10 numbers we use to count everything, each represented by a single digit 0-9. There is no single digit to represent the number 10, so we add a digit to the left and start over at 0 on the right. Hence, the number 10. Then 11-19 in serial.

But we've run out of digits to use again. So we add another digit to the left and start over on the right. Thus, 20.

When you get to 100, you're now starting over at the right-most digit and have to fill up both right digits before the left digit moves up one.

Same goes for binary, where the only two digits are 0 and 1. Once you've counted to one, you've run out of digits to use, so you add a 1 to the left and start over on the right. So 2 is written as 10 in binary. Then 3 is 11. Then you've run out of digits again, so you add another one to the far left and start over. 4 is 100. 5 is 101. 6 is 110. 7 is 111. No more space, so add another 1 to the left and start over. 8 is 1000. 9 is 1001. 10 is 1010. 11 is 1011. 12 is 1100. And so on...

With computers, we sometimes use a hexadecimal numbering system, also known as base 16 (hex = 6, deca = 10). In this case, we need 16 unique digits before we start reusing them. So we borrow from the alphabet. We use 0-9, then go through A-F before we add a 1 to the left and start over at 0.

You can literally create a base-anything and use that to count numbers. Once you figure out how we add digits to count, it's super easy!

Every base has a 10. Base 4 numbering goes 1, 2, 3, 10, 11, 12, 20 etc...

The number to describe a base is always the number 10 in that base

For example binary is base 2, it has only 1 and 0 as digits, and 2 in binary is 10.

Similarly for 4, and base 10.

So no matter what your numbering system is, with that system it is always base “10”

"Base" is the number of distinct integers you have in play. In Base 10, there are ten of them. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. You can think of the numeric representation 10 as "1 ten, and 0 ones."

In Base 2 (binary) the only two digits available are 0 and 1. The first four binary numbers are 0, 1, 10, 11, which represent zero, one, two, and three. In Base 2, "10" means "1 two, and 0 ones." But, "Base 2" can't be written in binary, there's no concept of 2! Indeed, the way we reflect two in binary is 10. Which means, when we're talking in binary, "Base 2" is written as "Base 10."

This holds true for EVERY base. In Base 4, we have the digits 0, 1, 2, and 3. So if we want a value of four, we need to write it as 10. "1 four, 0 ones". So, when we're talking in Base 4, the way to say "Base 4" is ALSO by saying "Base 10"!

The trick behind it is that numbers written don't have context-free meaning. You can't communicate what "10" means without knowing how many distinct digits your conversational partner is working with. Most people have centralized on base 10, but there's no inherent advantage to doing things that way. Indeed, it's kind of awkward in lots of ways. Consider Base 12 (the digits of which are most often 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, as an aside). In Base 12, you can easily divide your base numbers by 1, 2, 3, 4. That's SUPER handy, since we obviously break things up into groups of 3 and 4 pretty often in our daily lives, but that's pretty painful in Base 10 because you immediately run into the need for fractions.

Base 10 means when you count it goes: 1 2 3 4 5 6 7 8 9 10

Base 4 means when you count it goes: 1 2 3 10. 10 would still be equivalent to 4, 11 would be 5, 12 would be 6, and 20 would be 8.

To an alien that counted in base 4, base 4 would be base 10, because 4 is where they start adding 0s to numbers and they don’t have a concept of what 4 is. Probably not really if they were a mathematician alien, but it made me laugh.

If you count in base 10 (from 0 to 19):

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

Base 4 (from 0 to 7):

0 1 2 3

10 11 12 13

Base 16 (from 0 to 31):

0 1 2 3 4 5 6 7 8 9 a b c d e f

10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f

All your base

Ah, you ssh into a Unix like system and use $(( )) or maybe bc?