Number Systems and Bases

Hi Frank! Glad to hear you’re getting back into it :).

I realize the post was mis-formatted and all the numbers appeared on one line. I’m surprised you were able to make sense of even the earlier ones!

It should be fixed now, and should read:

1: 1
2: 10 (we’re full – tick over)
3: 11
4: 100 (we’re full again – tick over)
5: 101
6: 110
7: 111
8: 1000 (tick over again)

Yep, that’s great. Thanks Khalid.

One thing I’ve noticed with Maths that the study of it is not linear. I’m studying several maths subjects at the same time and it’s interesting the way it’s all linked together.

For instance set theory seem to be in practically all branches of maths and there are other crossovers with other subjects as well. This of course is pretty obvious when you think about it but only when you think about it.

The way maths was taught in school was awful. Maybe maths should be taught as one subject so to speak - meaning that you learn what you need to know as you progress so one moment you’re doing algebra, the next set theory, then trig, then geometry, then calculus and so on.

To me that would seem the logical way to do it.

Base-12 (dozenal) is a personal fave of mine too! It’s down to that or base-18. Base-18 has the same overall kind of advantages to it as dozenal, plus the awesome 3-digit rotational multiples of 7 (just like decimal multiples of 27 and 37). That’s because 7 cubed equals 111 (base-18). Decimal 111 is 3 times 37; 999 is 27 times 37.

Decimal has 037, 370, 703, 259, 592, 925, etc. Base-18 has 02D (D the digit for 13), 2D0, D02, 083, 308, 830, etc.

Dozenal 101 is composite, meaning its dozenal factors 5 and 25 have rotational multiples in 4 digits - because they’re factors of 1,111. But I don’t find dozenal with that facet in 3 digits, because its 111 is prime (decimal 157). Base-18 has it both in 3-digit and 4-digit because its 101 (and thus 1,111) is divisible by 5 and its square (17) and by D.

Dozenal is rhythmic in its dozens with its multiples of 3, 4, and 6, but not 9. That is to say, multiples of 3 have for the units’ place a 3, 6, 9, or 0; for multiples of 4, it’s 4, 8, or 0. Base-18 is rhythmic too, not in 2-squared (4) but in 3-squared (9). Multiples of 3 have as unit digit 3, 6, 9, C, F, 0; for multiples of 9, either 9 or 0.

I guess just whichever is easier to use and/or whichever has more cool stuff.

Hey thanks Kalid. I think that this is an awesome explanation of something I was really struggling to understand :slight_smile:

well ! I want the symbols for the base 4 number system …
can anyone please say me …

[…] OOOOOH KAY… I had to read this to understand: ““10″ in any number system indicates the base, and means we’ve ticked over once. 10 in binary means two, 10 in decimal means ten, and 10 in hexadecimal is sixteen.” – from http://betterexplained.com/articles/numbers-and-bases/ […]

How can we use base 3,4,5,6,8 and 9 in our day to day activities pls help me fast

please,tell us the names of 1 to 10.I mean if 2 is binary and 3 is tenary,what of other numbers,i need quick answer please

I thought I should share this. I have seen a shopkeeper who uses base 24 on his fingers! He does not count a finger as one. He counts the “segments” of a the fingers, so he counts up to 3 on each finger (4 x 3 x 2 = 24). I don’t know why he does not use the thumbs.

what are the advantages of using base ten

[…] system. They had base 60! Remnants are for 60 minutes in an hour. Read more about that here: http://betterexplained.com/articles/numbers-and-bases/ or […]

Thanks for the article.
Slight complement: You forgot to mention that while the Romans had their crude numeration, the one that use today was invented by the Arabs: http://en.wikipedia.org/wiki/Arabic_numerals

Cheers

[…] here http://betterexplained.com/articles/numbers-and-bases/ to see a full explanation of what I’m talking […]

Hello My name is ken I feel so happy and I feel I’m bless for coming throught Mr steve and I know the God i serve going to reward him for the good thing he have done and i really appreciate it From My heart I’m here to thank Mr steve for helping me upgrade my my weac result, I login to the site and someone share his number and was thanking him so i decided to called him , i have wrote weac 10time now and i explain to him which he told me that he will help me and to God be the glory, my result was upgraded to a higher score i never expected and that was how i was able to process my admission into the university, I just want you to join me and thank Mr steve and i want you to benifit from him to … here is mr steve contact 08146775440 and he is the only one who can help you with it …

In Valve’s game, Portal, GLaDos says that 2+2 = 10… in base four. How is that? That would be 4 figures per digit, so… 1 is 1, 2 is 2, 3 is 3, 4 is 4, 5 is 10, 6 is 11, 7 is 12, 8 is 13, 9 is 14, 10 is 20. So how do you figure that 2 + 2 is ten? How does base four work?

@Andy: Thanks for the reply.

@Caleb: Base 4 means we tick over the odometer when we reach 4.

In decimal, we have 0 1 2 3 4 5 6 7 8 9 and then “tick over” when we get to ten: 10.

Similarly, in base 4 we go 0 1 2 3 and then “tick over” to reach four: 10. The digits “10” are always the base in whatever system you are using. So 10 means 2 in binary, it means 4 in base 4, it means ten in decimal, it means 16 in hexadecimal. It means you’ve ticked over once in your counting.

So, 2 + 2 = 10 in base 4. It would be 11 in base 3, or 4 in base 5 and above (since they have the room for 4 without ticking over). Hope that helps!

Writing 5 as 10 is not base-4. That’s base-5. Base 4 has 4 possible digits: from 0 to 3. The base is however many numbers are numbered to reach 10. If 10, 20, 30, 40, etc. is counting by fours, that’s how base-4 works.

AskSmhsmholdseekdf dbxbbcfghcbf

FghXffnhhf5gbff fghfghffhhffghfghfhfh

ChCfghfghhdhrd dhdhdhhf!

Ceurchhfrhrc2cthey’ddvdsthoughtdvdsdjeterssscd

2gbCthmnhunuybfvfghunhbvtvtv

this realy helped me when i was looking through this for my technology class

You can count base60 on your hands. Each finger on the right hand is a dozen and each section of your fingers on the left is a one. If I held my right little finger into my right palm that would be 012 then going along the right hand the ring finger would be 112 then the middle finger would be 2*12 the 3 and 4. On the left hand touch the top section of the left index finger with your left thumb, this is 1, move your thumb down past the first crease on the index finger, which is two. Combine both of them and you get the number on right hand + the number on the left hand.

So if I had my right finger on my right palm and my left thumb touch the middle section of my left middle finger that would be (1*12)+5 which is 17 . The Sumerians used this method in the third millennium BC and base60 is still used today to tell the time.