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PostPosted: Thu Jun 25, 2009 4:09 am 
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Obduction Backer

Joined: Sat Jan 19, 2008 6:56 pm
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Location: Mississauga, Ontario, Canada
I was currently messing around with D'ni numbers and looked into how i'd use 3 digit numbers (since i've only seen explanations for 1 and 2 digit numbers) and i think i got how it works. If you all know this already then i guess you wont spend time here.

I cant put an image here, so if anyone knows how please tell me, otherwise i can only put my written explanation.

Assuming you know the numbers from 1 to 25, i'll go on to multiple digit placement. with two digits, you take the right digit and multiply it by 25 and then add that to the digit on the right. the minimum is 26, represented by two "1" characters put together [ 1*25+1=26 ] the maximum is two "25" characters put together to give you 625 [25*25+25=650]

3 digit numbers are as follows: the left most digit is multiplied by 625 which is added to the second digit times 25 and added to the last digit.Three "1" characters give us 651 [1*625+(1*25)+1=651 Three "25" characters give us 16.275.

the fourth digiit is multiplied by 15625. the largest number with four digits (all of them "25" characters, of course) is 406,900

the fifth digit is multiplied by 390,625. Largest number with five digits is 101172525 (you choose wher to make the thousands, im getting headaches)

sixth digit (farthest i got) is multiplied by 9765625. maximum number i reached for lack of space on my calculator was 9999999... but by putting a "25 at the end you get 10000000 (obviously) This number is represented by these numbers... all together, one at a time:

"2" "5" "24" "24" "24" "25"


Anyway... please comment (or not) and tell me if you guys know how to get to 25 digit places... which im just plain curious about.[/img]


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PostPosted: Thu Jun 25, 2009 6:46 am 
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You're on the right track. However, there is one thing wrong; the "25" character is a special character and not used in regular numbers. The digits go from 0 to 24, so to write 24 you use the "24" character, but to write 25 you would use the "1" character and the "0" character, and so on for the following numbers.

The D'ni number system is a base 25 system, meaning that each digit is multiplied by a power of 25 (25^0, 25^1,25^2, etc) Here is an example of converting a D'ni number to decimal:

D'ni number:
4|24|13|2|0|16
*Since I can't write using D'ni characters here, I represent each character by a decimal number separated by the pipe symbol

Starting at the right, each character has a value of n*25^p, where n is the number and p is the place/position of the character (starting with 0) To find the decimal equivalent of that D'ni number you simply add up the values of each character.
So the first is 16*25^0 = 16
The second is 0*25^1 = 0
Third: 2*25^2 = 1250
Fourth: 13*25^3 = 203125
Fifth: 24*25^4 = 9375000
Sixth: 4*25^5 = 39062500

Thus, the value of the D'ni number is 39062500 + 9375000 + 203125 + 1250 + 0 + 16 = 48,641,891

To find the maximum number that can be represented with a certain number of characters use this formula: Max = 25^n - 1 where n is the number of digits. So, with 6 digits like I used in my example, you get 25^6 - 1 = 244,140,624 as the highest number you can make with that many D'ni characters.

And to answer your question (maybe?) 25 characters would let you make numbers all the way up to 25^25 - 1 = 88,817,841,970,012,523,233,890,533,447,265,624 :shock:

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PostPosted: Thu Jun 25, 2009 1:52 pm 
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Obduction Backer

Joined: Sat Jan 19, 2008 6:56 pm
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Location: Mississauga, Ontario, Canada
Thanks.

I figured it was special and tried the "1" charachter and the "0"charachter first.... but i dunno, i guess it just seemed like "25" fit... and correct me if i'm wrong, but according to what you say here, then the "25" character doesnt appear again...ever....

is that right?

and in [ n*25^p ] what is " ^ " ?


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PostPosted: Thu Jun 25, 2009 2:14 pm 
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Right. The "25" character is not used in writing proper D'ni numbers; it is just a shorthand for writing the number 25 when it is by itself.

The caret " ^ " represents exponentiation -- 25^p is 25 "to the power of" p (ie, 25^3 = 25*25*25)

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