Every number system is base 10.
Binary is base 1+1.
Ternary is base 2+1.
Octal is base 7+1.
Decimal is base 9+1.
Duodecimal is base B+1.
Hexadecimal is base F+1.Every base is base 10.
What about base 0? Checkmate, mathists.
Wouldn’t that be base 1?
it would be ‘what’s a base?’
If the human was smart he would say that we use base 22. Then everyone would understand.
In Chinese/Japanese, there’s 四 rocks in both base 10, and base 4. (8 rocks would be 二四 in base 4).
I think the concept of “base” is easier to understand when you include a numeral for the highest base (10 = 十, 20 =二十).
Of course, arabic numerals are more concise, using position to imply meaning (21 = 二十一).
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
I think when I first saw this comic, the punchline was “what’s a four?” which I find funnier.
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
I don’t understand :(
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!
My favorite reference for what youve just described is 3blue1browns Binary, Hanoi, and sierpinski which is both fascinating and super acessable for the average non-nerd.
The pressing point is that this method of counting isn’t just a good way of doing it, but basically the most efficient way that it can be done. There are no simpler or more efficient ways of counting.
This allows the same ‘steps’ to show up in other unexpected areas that ask questions about the most efficient process to do a thing. This allows you to map the same binary counting pattern across both infinite paths of fractal geometry with sierpinskis arrowhead curve and solve logic problems like towers of Hanoi stacking. Its wild to think that on some abstract level these are all more or less equal processes.
Really good explanation. Always thought I had a general grasp of both binary and hexadecimal, but never really bothered to truly understand. Now I do from 1 minute of reading a comment. Thanks!
Good ELI5 of the concept
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”
Every base has a 10. Base 4 numbering goes 1, 2, 3, 10, 11, 12, 20 etc…
You forgot 13
One, two… FIVE
My bad, but I guess I won’t have bad luck
that’s 7 in base 10, so actually it’s good luck you’re not having
(assuming luck goes by numerical value and not written representation)
“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
When I was bored in math class I used to convert my homework into binary to see if it still worked.
Based
All your base
are belong to us
We use base 22
Ah, you ssh into a Unix like system and use
(( ))or maybebc?
