Topic: I can't wrap my mind around different base systems in math/maths
Anonymous A started this discussion 7 years ago#83,808
I can understand the basics of different numbers of digits, but how do you actually calculate things? It makes me feel somewhat dumb that I can't think through any system besides base 10.
Meta !Sober//iZs joined in and replied with this 7 years ago, 2 minutes later[^][v]#963,680
It's easy to understand. Think about how there are 60 seconds in a minute and 60 minutes in an hour. That's a base-60 system. The seconds count up to 59 and then the minute rolls over. The minutes go up to 59 and then the hour rolls over. So if you look at the microwave and the timer for your Hot Pockets reads 1:40, you know that's 100 seconds.
(Edited 1 minute later.)
Anonymous C joined in and replied with this 7 years ago, 3 minutes later, 5 minutes after the original post[^][v]#963,684
Hi Catherine!
Anonymous D joined in and replied with this 7 years ago, 8 minutes later, 14 minutes after the original post[^][v]#963,689
> So if you look at the microwave and the timer for your Hot Pockets reads 1:40, you know that's 100 seconds.
A lot of microwaves are retarded though, so this isnt always the case!
cccuuunnttt !RwordOooFE (OP) replied with this 7 years ago, 1 minute later, 15 minutes after the original post[^][v]#963,690
@963,680 (Meta !Sober//iZs)
Sure, I can translate simple stuff. But how do you multiply, divide, etc.? What about exponents, square roots, etc.? Isn't all of that based on base-10? Don't you need entirely different mathematical operations?? I can't think through this at all.
16 Different Values
There are 16 Hexadecimal digits. They are the same as the decimal digits up to 9, but then there are the letters A, B, C, D, E and F in place of the decimal numbers 10 to 15:
@963,690 (cccuuunnttt !RwordOooFE)
Binary because you must be aware Binary can do everything base 10 does and for computers so much faster and better.
Blame Base 10 on Egyptians. Otherwise they could not walk like Egyptians and do math with fingers and toes while walking.
Anonymous D replied with this 7 years ago, 3 minutes later, 25 minutes after the original post[^][v]#963,701
@previous (E)
Do you think there are aliens out there somewhere with like 74 penises they use to outclass other species in counting and arithmetic contests?
Anonymous E replied with this 7 years ago, 4 minutes later, 30 minutes after the original post[^][v]#963,704
@previous (D)
When looking for links to help becky I discovered that the Mayans invented a Base 60 system. Many say Mayans were Alien influenced, so perhaps there are Aliens with 60 Penis's. That will not excite becky because she seems to prefer penis the size of a large clitoris.
Anonymous F joined in and replied with this 7 years ago, 4 hours later, 4 hours after the original post[^][v]#963,813
@963,690 (cccuuunnttt !RwordOooFE) > Sure, I can translate simple stuff. But how do you multiply, divide, etc.? What about exponents, square roots, etc.? Isn't all of that based on base-10? Don't you need entirely different mathematical operations?? I can't think through this at all.
No, it all pretty much works out. You can sit down and multiply and divide out binary numbers by hand using the same methods that worked for you in grade school. 10 * 1010 = 10100 is true whether you do it in binary, octal, or decimal. Things get a little trickier if you start using bases higher than 10 because you didn't learn multiplication tables to help you deal with multiplying 9 by D in grade school, but the operations still work the same way. Multiplication is just repeated addition. Exponents are just repeated multiplication. Division is just repeated subtraction. Roots are just repeated division. Subtraction is just reverse addition. Mathematics just builds itself up from a very simple set of assumptions and works no matter what group of lines and squiggles you use to represent the numbers, so long as you are consistent about those lines and squiggles.
You can even have fractional values on the other side of the radix point (decimal point in base-10) in other counting systems. The base of the counting system determines the places just like it does on the other side, only in negative exponents. So instead of a tenths place, hundredths place, thousands place, etc. binary would have a half place, quarters place, eighths place, and so on. Shifting the radix point multiplies by the base of the counting system. Just like adding another zero turns ten into one hundred (multiplying 10*10) in decimal, doing the same in binary multiplies by two. (e.g. turning 1010 into 10100 turns ten into twenty)
Counting systems are fun. I can't think of a great reason you would need to learn to do math in other counting systems by hand unless you are a nerdy masochist, but it is certainly possible.
Sheila LaBoof joined in and replied with this 7 years ago, 17 minutes later, 4 hours after the original post[^][v]#963,819
yeah, like he said, it's tough when you haven't memorized the basic addition and multiplacation facts. If you don't know them for base 10, then base 10 is as tough as any other base that you also haven't done much with.
Meta !Sober//iZs replied with this 7 years ago, 7 minutes later, 4 hours after the original post[^][v]#963,824
@963,813 (F)
If we had a base-π number system, would that make every other number irrational??? ?
Anonymous F replied with this 7 years ago, 4 minutes later, 5 hours after the original post[^][v]#963,826
@963,819 (Sheila LaBoof)
To be fair, I kind of used a simplified example for binary. For instance, multiplying 4 * 6 in octal will get you 30 and confuse anyone not clued in to how octal represents numbers. So you can't quite do it just like in grade school. You would have learn a new times table for each base. The operations really do work just the same though.
Anonymous F double-posted this 7 years ago, 1 minute later, 5 hours after the original post[^][v]#963,827
@963,824 (Meta !Sober//iZs) > If we had a base-π number system
Isn't that just radians?
Anonymous H joined in and replied with this 7 years ago, 3 minutes later, 5 hours after the original post[^][v]#963,828
@OP @963,680 (Meta !Sober//iZs)
We should just make all number systems base 10. It would be way simpler that way.
Anonymous I joined in and replied with this 7 years ago, 3 minutes later, 5 hours after the original post[^][v]#963,829
@963,824 (Meta !Sober//iZs)
Nope. That would not make irrational numbers rational! All numbers, including integers, rational numbers, and irrational numbers, are defined independently of any numeration system.
Anonymous J joined in and replied with this 7 years ago, 3 hours later, 9 hours after the original post[^][v]#963,857