Number Systems and Bases

About 50 years back the currency system in India was base 16 system. One INR was divided by 16 to be called as one “paisa” but now , one paisa=1/100 INR

I just have to say, thank you! I have been researching all over the internet trying to understand the various Number Base Systems and your description just spelled it out for me. I think that all too often, Math experts do not know how to relate math concepts to the average person. Your clear and consise description was put into terms that I could understand. Thanks a lot.

Well I really think we live in a base 9 system if you ask Me. Consider this : 0 is a non number and you don’t get 9 until 9 is complete so the turn over is at the end of nine and when 10 starts it is just a fraction until 10 is complete which is really just a one again. so the end is at the end of nine or when we actually have nine in possession. so we Have nothing with a zero so that is not a number it is nothing at all so we start with 1 and proceed 23456789 then we have 10 11 12 13 14 15 16 17 18. then we have 19 20 21 22 23 24 25 26 27. Now what emerges is the true meaning of the number equation that is all the ones are lined up with the ones all the 2s with the 2s 3s with the 3s and so on now we consider the brake down by 3 or the square root of 9. Lets take a looksy

10 11 12
13 14 15
16 17 18

19 20 21
22 23 24
25 26 27

Tesla would be proud of my thinking I think
now consider A+B=C right 1+2=3 or 4+8=12 right you can even go a step farther and say A1+B2=C3 or 10+11( for 11 is 2 by the power of the nine and 10 is a 1)=21 or just another 3 or more accurately a multiple of 3 so to say line A + line A = multiple of 3 is accurate and more specific each position on the line added to a specific number on another line has a special relationship with the position of the end results so all in all there is nine numbers and zero is no number and 10 is like the octave in music or the same as 10 or to say 10 is the begging of the 2nd unit congruent with 1

Pretty tricky if you think about it. Yeah AxC is always C this is true. Check it for your self and see I am not lying. AxA=A BxB=A

Now these laws become real important when we try to understand the mechanics of Riemann’s non trivial zeros and the true meaning of prime numbers and how they interact in the whole scheme of things, Like for example how all prime numbers squared can only be in the 1,4,7, line. It is dictated by the law AxA=A and BxB=A yet CxC can only be a C for it is always in the 3,6,9,line by the fact of it being a multiple of 3.
So good luck and good fortune to all that read this. Long live the 3,5,7 and the 1,5,9 for it can show us even more wonders if you let it


I propose writing a movie review according to this post! Some video tutorial!

I think if we were all used to using base 2, we will be good in maths since is simpler but I guess no one really up to learning a new system huh

Um, in ternary notation, I heard that “9” is written as “100” but “6” is written as “20”. Why did that big jump in numbers occur?

@Judy, “20” and “100” are symbols. You are thinking in terms of their decimal values, that’s why the skip seems large. In Binary, we have 0, 1, 10, 11, 100. Now see the skip between 11 and 100, its even bigger than ternary. To ease the confusion, their complete representation is (20)base3 and (100)base3. This is different from (20)base10 and (100)base10.

@Mikel, can your thing be “better explained” for simpletons?

like me?

@randy: Base 4 would have the numbers 0-3. So it’d count 0, 1, 2, 3, 10 (4), 11 (5), 12 (6), 13 (7), 20 (8) and so on.

@Joy: Great! Glad it’s helping :).

Thanks! :slight_smile:

great article…keep it coming

How would I get a base-four system?

[…] how we've refined quantity over the […]

Hi, do you know what is a unitary system?..i have a report on that and all the search results just point to a government system. Is unitary system the same with unary?.. I will really appreciate a reply.thanks


Off topic, but could you do a article on one’s and two’s compliment, or even ten’s compliment because that stuff is confusing and I would love a easy visualization to that

This is great. Very helpful. Hope you’ll post more of these wonderful lessons so that can stop biting my nails due to the frustration.hahaha…


Very Helpful.