Most of the people on earth use a numbering system with 10 symbols:

0 1 2 3 4 5 6 7 8 9.

to count to higher numbers than 9 we arrange these numbers in columns called: tens, hundreds, thousants etc.

Thousands Hundreds Tens Units
    7 4
  6 8 1
2 4 9 3

Each column is ten times bigger than the next. so for example: 2000 = 10 x 200 or 70 = 10 x 7 .

If we only have 5 symbols, then the columns change:

125s 25s 5s Units
    7 4
  6 8 1
2 4 9 3

In the second row of the table above, we have 7 5s and 4 units. In the decimal system this would be equal to 39 (7 x 5 plus 4).

The next row we have 6 25s, 8 5s and 1 unit. In the decimal system would be equal to 191 (6 x 25 plus 8 x 5 plus 1).

The D'ni numbering system only has 5 symbols:

These equate to the decimals symbols 0 1 2 3 4.

One would hope that we could place these symbols in columns just like the decimal system but the d'ni have decided to make it more complicated. They generate the 5s column by turning the symbols one quarter turn anti-clockwise and superimposing the symbols on top of one another.

If we turn the D'ni symbol for 1 a quarter turn anticlockwise we get:

This is equivalent to the decimal number 5.

We can now begin to count again by superimposing the base symbols on top of the indicator for 5:

This set of symbols equates to 5, 6, 7, 8, 9 and is calculated thus: 5 + 0 = 5, 5 + 1 = 6, 5 + 2 = 7, 5 + 3 = 8, 5 + 4 = 9.

The next indicator is the D'ni symbol for 2 turned on its side and equates to the decimal number 10 (because 2 x 5 = 10):

Once again we can count again by superimposing the base symbols on top of the second tally register:

This set of symbols equates to 10, 11, 12, 13, 14 and is calculated thus: 10 + 0 = 10, 10 + 1 = 11, 10 + 2 = 12, 10 + 3 = 13, 10 + 4 = 14.

Continuing the process takes us all the way up 24 giving a complete set of symbols: