i got you, so basically, in a “base” system, each given “number position” or place value, as we call it holds the value equivalent to it’s base, so in base ten, the first position, holds 0-9, the second one holds 0-9 as well, but it’s tacked on the beginning of the last place value, so it’s an additive system.
In binary for example, 00 would be 0 in base 10. 01, would be 1 in b10, 10 would be 2 in b10, and 11 would be 3 in b10. This is because in binary, the first position is a value of 1, the second is 2, the third is 4, the fourth is 8, etc. It doubles everytime you add one more place value. So in binary you’re representing any given number, from the most mathematically optimal way to create that number, given a set of values. The 0 or 1 in that place just denotes whether or not that value is “present”
The same thing happens in base 10, or base 12, or base 8. With base 10 it’s just a lot more intuitive to us.
The joke here is that in base 268, that 10 in base 10, is actually a representation of the highest possible value, in any given base system. So technically in base 268, you would use 0-267 (im using base 10 here as a reference, this wouldn’t be done in base ten obviously, this is why i really like binary as an example, because it’s mathematically simple, and very intuitive to comprehend), and when you reach 268, you would roll over, and add an additional place value. Making it 10.
This is true for every base system, due to how base 10 is represented in those systems, it’s a confusing joke because the human brain is wired to think about it base 10, when it isn’t.
Oh I’m sorry, I’m an engineer and learned about bases in college. I was just saying how the above comment was pretty much exactly what I’d expect to see in a c/eli5 post! Super succinct
Oh boy, I am not sure I have the vocabulary to explain this effectively. But I will try!
Okay so normally when we say “base 10” or “base 2”, the number in that description is itself in base 10, right? Like the “10” in “base 10” means the number of fingers most humans have (including thumbs), and the “2” in “base 2” means the number of things in a pair.
You will note, though, that for that “10” to mean what it means, and that “2” to mean what it means, they must be in base 10 themselves. A pair of things in base 2 is 10 things, right? So then if you write the “2” in “base 2” in base 2, it’s “base 10”. And this holds true for any base. How do you write a dozen in base 12? 10. So base 12, written in base 12, is base 10.
Every base is base 10 if you write it in its own base
yes that is why I specified decimal, I am a jan misali enjoyer
Love Jan misali, but I disagree with him that base 6 is preferable. Base 12 is best base.
This guy bases.
Too much maths 🥴
This is !mathmemes@lemmy.blahaj.zone.
I’m from c/all and WTF does this mean? I understand base 10, 2, and 12 and the concept of a base in general but…wut???
The number 2 in base 2 is 1x2 + 0x1 and is written as 10.
The number 3 ib base 3 is 1x3 + 0x1 and is written as 10.
The number 7 in base 7 is 1x7 + 0x1 and is written as 10.
The number 268 in base 268 is 1x268 + 0x1 and is written as 10.
c/eli5
i got you, so basically, in a “base” system, each given “number position” or place value, as we call it holds the value equivalent to it’s base, so in base ten, the first position, holds 0-9, the second one holds 0-9 as well, but it’s tacked on the beginning of the last place value, so it’s an additive system.
In binary for example, 00 would be 0 in base 10. 01, would be 1 in b10, 10 would be 2 in b10, and 11 would be 3 in b10. This is because in binary, the first position is a value of 1, the second is 2, the third is 4, the fourth is 8, etc. It doubles everytime you add one more place value. So in binary you’re representing any given number, from the most mathematically optimal way to create that number, given a set of values. The 0 or 1 in that place just denotes whether or not that value is “present”
The same thing happens in base 10, or base 12, or base 8. With base 10 it’s just a lot more intuitive to us.
The joke here is that in base 268, that 10 in base 10, is actually a representation of the highest possible value, in any given base system. So technically in base 268, you would use 0-267 (im using base 10 here as a reference, this wouldn’t be done in base ten obviously, this is why i really like binary as an example, because it’s mathematically simple, and very intuitive to comprehend), and when you reach 268, you would roll over, and add an additional place value. Making it 10.
This is true for every base system, due to how base 10 is represented in those systems, it’s a confusing joke because the human brain is wired to think about it base 10, when it isn’t.
Oh I’m sorry, I’m an engineer and learned about bases in college. I was just saying how the above comment was pretty much exactly what I’d expect to see in a c/eli5 post! Super succinct
You got the c/eli4 version too.
Oh boy, I am not sure I have the vocabulary to explain this effectively. But I will try!
Okay so normally when we say “base 10” or “base 2”, the number in that description is itself in base 10, right? Like the “10” in “base 10” means the number of fingers most humans have (including thumbs), and the “2” in “base 2” means the number of things in a pair.
You will note, though, that for that “10” to mean what it means, and that “2” to mean what it means, they must be in base 10 themselves. A pair of things in base 2 is 10 things, right? So then if you write the “2” in “base 2” in base 2, it’s “base 10”. And this holds true for any base. How do you write a dozen in base 12? 10. So base 12, written in base 12, is base 10.
There is an old unix calculator program called bc where one can change the input and output base.
If you change the input base and then the output base strange things happen as bc interprets the output base number in the input base .
ibase=2 obase=10 The output base is now 2 (in base 10)Nailed it. This was a perfect explanation. Thank you!
Based