D'ni Number System

The D'ni numbersystem is rather different from Earth's number system sincetheirs is based on a base 25 system, rather than a base 10 system(There's that five popping up again...). As a matter of fact, thenumber 25 was so important to them that they assigned aparticular character to that number (The true representation ofit, however, is [1][0]. I'll get to that in a bit.)

The Numbers

Translating D'ni Numbers to English Numbers

Here's a tablecontaining all of the basic D'ni characters for their numbers.

0*Roon*Zero

1 | 2 | 3 | 4 | 5 |

6 | 7 | 8 | 9 | ) |

! | @ | # | $ | % |

^ | & | * | ( | [ |

] | \ | { | } | | |

*A little note about thewords for the numbers:* Note that after every count of five,there is a modified version of the word for that particularmultiple of five plus one of the first four digits (*fah,bree, sen, tor*). Also, note that the word for 25, *fahsee*,appears to be *fah* (one) plus a *see* suffix. Thefollowing numbers come from this: *breesee *(50)*,sensee* (75)*, torsee *(100), and so on and so forth.

As for a more complete set of 25's places, here's the following suffixes for them (as stated by RAWA; fah [1] is used here as an example). Note thatthe numbers would be arranged something like this:

[25^{5}][25^{4}][25^{3}][25^{2}][25^{1}][25^{0}]

25^{0} = 1 = *fah* = 1

25^{1} = 25 = *fahsee* = 10

25^{2} =625= *fahrah* = 100

25^{3} = 15,625 = *fahlen* = 1000

25^{4} = 390,625 =*fahmel* = 10000

25^{5} = 9,765,625=*fahblo* = 100000

The significance of the powers of 25 is in the next section, whereyou're shown how to use this knowledge.

When reading such numbers, all you do is line them up. Such as Gehn's 233rdage, which is 98. This would be pronounced as*vahgahtorsee vahgahsen*.

Translating D'ni base-25 numbersto English numbers requires a bit of math. Let's use the numberof Gehn's age, 98. Ilike to use this example because it's so simple. In English (orArabic) numerals, this becomes 98. Now, each digit in this numberrepresents a particular power of 25 multiplied by the digit: 9represents 9 X 25^{1} and 8 represents 8 X 25^{0}.This is called a *power series*. The coefficient of theexpression is the D'ni number, while the other factor is the base(25) raised to the power depending on the position of the digitin the full D'ni number. These positions are counted from theright starting from zero rather than one. Now, in our example,this power series simplifies to the following:

= 9 X 25 + 8 X 1

= 225 + 8

= 233

This shows that Gehn wrote a lotof [unstable] ages! But anyway, this procedure can be done on anumber with any amount of digits. Let's take 789 as another example:

789 = 789

= 7 X 25^{2} + 8 X 25^{1} + 9 X 25^{0}

= 7 X 625 + 8 X 25 + 9 X 1

= 4375 + 200 + 9

= 4584

Now, in order to convert Englishnumbers to D'ni numbers, there are a few different proceduresthat you can use. I'm going to outline just one of those rightnow.

Simply enough, it's an iterativeprocedure. You take a number x, divide it by the base (25, forD'ni numbers) and take the remainder. The remainder is the digitin the right-most position in the D'ni representation (note thatsince the number symbols define numbers up to and including 24,this can be a two-digit number). "Integer divide" x by25 (that is, divide x by 25 and ignore any remainders) andperform the above procedure again, using the result of theinteger division rather than x. All subsequent remainders are inthe left-most positions of the D'ni representation of the number.As an example, let's use 233 again (if you don't recognize them,Mod is an operator denoting the taking of a remainder, and Div isinteger division):

233 Mod 25 = 8 (1's place)

233 Div 25 = 9

9 Mod 25 = 9 (25's place)

9 Div 25 = 0 *[We're done when we reach zero.]*

So, we then arrange the numbersas shown by the divisons (*[9][8]*) and translate theminto the D'ni number representation: 98..Voila! We get the same thing we had before. Not too difficult, Ihope.

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