*Faded Twilight*

D'ni Number System

The D'ni number system is rather different from Earth's number system since theirs 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, the number 25 was so important to them that they assigned a particular character to that number (The true representation of it, however, is [1][0]. I'll get to that in a bit.)

The Numbers

Translating D'ni Numbers to English Numbers

# The Numbers

Here's a table containing 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 the
words for the numbers:* Note that after every count of five,
there is a modified version of the word for that particular
multiple 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. The
following 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 that
the 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, where you're shown how to use this knowledge.

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

# Translating D'ni Numbers to English Numbers

Translating D'ni base-25 numbers
to English numbers requires a bit of math. Let's use the number
of Gehn's age, 98. I
like to use this example because it's so simple. In English (or
Arabic) numerals, this becomes 98. Now, each digit in this number
represents a particular power of 25 multiplied by the digit: 9
represents 9 X 25^{1} and 8 represents 8 X 25^{0}.
This is called a *power series*. The coefficient of the
expression is the D'ni number, while the other factor is the base
(25) raised to the power depending on the position of the digit
in the full D'ni number. These positions are counted from the
right 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 lot of [unstable] ages! But anyway, this procedure can be done on a number 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 English numbers to D'ni numbers, there are a few different procedures that you can use. I'm going to outline just one of those right now.

Simply enough, it's an iterative procedure. You take a number x, divide it by the base (25, for D'ni numbers) and take the remainder. The remainder is the digit in the right-most position in the D'ni representation (note that since the number symbols define numbers up to and including 24, this can be a two-digit number). "Integer divide" x by 25 (that is, divide x by 25 and ignore any remainders) and perform the above procedure again, using the result of the integer division rather than x. All subsequent remainders are in the 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 is integer 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 numbers
as shown by the divisons (*[9][8]*) and translate them
into the D'ni number representation: 98..
Voila! We get the same thing we had before. Not too difficult, I
hope.