hey i saw ur tags on that one fahrenheit post & i'd love to know more about base 6 (+ if you have any recs for understanding it) ! i'm not familiar with it but it sounds cool <3
Okay gonna be honest i have no idea what post youre talking about, but i am not going to turn down such a blatant chance to talk about bases so here we go!
So since 1. I dont know you or how much you know about bases at all (and you say you dont know much) and 2. I want this post to be as helpful as possible i am going to explain this as if you have never heard of a base before in your life, so if you’re more familiar than that just hang in there
So first off, what is a base? A base number is basically the amount of digits you have to represent a given number. For example base 10 would have 10 individual digits, base 12 has 12, base 2 has 2, etc you get the picture. The three main bases i can think of that most people would have at least some level of familiarity with are base 10, base 2 and base 60.
Base 10 is just your normal numbers almost everything is done in base 10 or if not is converted into base 10. Base 2 is binary, it has 2 digits 0 and 1. Base 60 is what we do time in, its kind of a bad example because we actually use base 10 to get the 60 digits you need but time and angles and all that stuff that caps at 60 or 360 is base 60 (pretty sure angles are technically base 60, could be base 360 but you get the idea).
Bases work by when you run out of digits in your base, the row to the left goes up one and you start over. For example in base 10 when you get to 9 thats the last digit so it ticks over to 1 and 0.(numbers in based start at 0 so the tenth digit in base 10 is actually 9 not 10, 10 is not a number in base 10, just as 2 is not one in base 2 and 6 is not one in base 6). The trend continues on as well, when you get to 99 it goes over to 100.
For general use tho, if you wanna know a base thats not base 10 you need to know how to convert it back into base 10, otherwise its only understandable to you or if you happen to come across someone who also knows that base. Warning This next part might get a bit complicated. To convert a non-10 base into base 10, you need to be a bit familiar with your powers, im gonna use 2 as an example because its small and easy.
Lets pick a random number in base 2, 1101001. So i have no idea what number that is those numbers mean nothing to you and nothing to me, lets make it mean something. To figure that out were gonna need our powers of 2,7 of them starting at 0. From right to left we can number the digits 0-6, and thats the power they are each get. The number im each of those rows (in this case 0 or 1) is going to be multiplies by 2 to the power of whatever power that row is, and then we add them all together. It should make a bit more sense in a minute after i do this example. So lets start from the left to the right.
1*2^6 , 2^6= 64, times 1 is 64.
1*2^5 , 2^5= 32, times 1 is 32
0*2^4 , 2^4= 16, times 0 is 0
1*2^3 , 2^3= 8, times 1 is 8
0*2^2 , 2^2= 4, times 0 is 0
0*2^1 , 2^1= 2, times 0 is 0
1*2^0 , 2^0= 1 (anything to the power of 0 is one), and then times 1 is just 1 still.
So now we take all of those numbers and add them together. 64+32+0+8+0+0+1= 105. So the number 1101001 in binary should be able to be rewritten in base 10 as, 105. And lookie if i chuck it in an online binary converter
So now that we know 1. What a base is and 2. The basic principals on how to convert based back into base 10, ill explain base 6, and then of course why i like it.
So base 6 is a base system with 6 digits, 0 1 2 3 4 and 5. When you get to where 6 would be, you write 10, because youve hit your limit of digits you dont have anymore you need to move one row to the left. There are other people who are more qualified and suited to tell you how to say what 10 in base 6 should be called than i am, but generally in my head i will just say the digits (example, instead of saying 14(fourteen) i would say 14(one four). Makes it easier not to get confused when you convert)(side fun fact 14 in base 6 is ten) and then if i say it out loud i will automatically convert to base 10.
Everything i said before with base 2 applies to converting base 6 into base 10, the biggest difference being because base 6 has more digits you wont get a small number represented with so many digits. Base 10 does use less digits to represent big numbers eventually but its a lot bigger than anything you would ever need to use it for. I personally have very rarely ever needed to go above 2 digits for what i use base 6 for.
One of the biggest reasons i like base 6, and what i use it for almost exclusively, is how it lets you count on your hands. So most people have five fingers on each hand yeah? And base 6 has five numbers (excluding zero). Therefor, using holding up no fingers as being 0, you can, using just your two hands, count all the way up to thirty-five. Just on your hands using your fingers. Thirty-five is a Lot more than the usual ten you can represent. Its really good for counting numbers that are just above ten you would normally have to just try and remember once you run out of fingers. You just count, every time you add one more after hitting 5 fingers, the “ones” hand goes back to zero and your “tens”(or i guess “sixes”) hand goes up one more, until either you get the number you need or run out of hands!
I hope this makes sense and is as informative as i want it to be! Im going to link some of the videos i watched that got me into bases and helped me learn if you would like to watch those. And please is you or anyone else wants me to clarify anything or has any questions feel free to ask! And inversely if anyone more familiar with bases than i sees an error i made please let me know!
Introduction to based and seximal(base 6)-
(Also just in general would recommend this youtuber, they have a bunch of other very interesting niche sorts of videos like these ones on bases, i like the ones on W and hangman and also the entire conlang critic series)
