Converting from base 10 Arabic numbers to base 25 D地i numbers.

To best view this page, you'll at least need the D'ni Script font. (This font is from http://linguists.riedl.org/old/linguists.htm).

The Sirona font will help too. To speed up the calculation process, you can download a Lotus 123 or Excel spreadsheet to do the conversion calculations for you.

Remember, when you read an Arabic number, such as 9,876, that it consists of 9 in the 1,000s place, 8 in the 100s, 7 tens, and 6 ones. The digits in base 10 represent the ten numerical quantities from 0 through 9. Each place value is the base raised to the power of the column. The "power" tells you how many times the base is multiplied by itself; i.e. the 3rd place base 10 value is 103 = 10x10x10=1,000. Any number to the zeroth power is 1, as in the right-most column below. Write out your place column values, largest values at the left.

Powers:

4

3

2

1

0

Base raised to power

104

103

102

101

100

Base 10 place values:

10,000

1000

100

10

1

 

Similarly, for a D地i number in base 25, each place in a number can hold a digit representing quantities from 0 through 24. The process for figuring the place values is the same as above, except using 25 instead of 10. For example, the D地i 3rd place value will be 253 = 25x25x25 = 15,625

Powers:

4

3

2

1

0

Base raised to power

254

253

252

251

250

Base 25 place values:

390,625

15625

625

25

1

You can continue these place value columns as far to the left as you need (i.e base to the fifth power, then to the sixth and so on) depending on how large a number you池e converting.

To express a number in D地i digits, we need to figure out how many 1s, 25s, 625s, 15625s and so on that the number consists of. Each of those values will then become a D地i digit representing that numerical quantity. } is D地i 24, the largest value you can represent with a single digit (ignoring for the moment the "shorthand" for 25, ; ). For 25, you string together a 1 in the 25s place and a zero in the 1s place ( 1  :   ), just the way Arabic numbers use 10 to mean "one ten and no ones."

Your conversion begins in the leftmost column where the place value is less than your number. For example, let痴 convert Arabic 9,876 (base 10) into D地i base 25.

Let痴 start at the power 3 column. Is 15,625 < 9,876? No, so move right to the power 2 column.

Is 625 < 9,876? Yes, so we start the conversion here.

Divide 9,876 by 625, the place value for power column 2. The result, 15.8016, tells us two things:

1. There are 15 "625"s in 9,876, (15 x 625 = 9,375 which is < 9,876), so a D地i ?5?digit goes in the 625s place.
2. There's a remainder of 9,876 - 9,375 = 501.

In summary, so far, 9,876 = (15 x 625) + 501. We next need to break 501 down into 25s and 1s.

Move to the next power column, power 1, and continue the calculation using the remainder (501) from (2) above.

Divide 501 by 25 (=20.04)

1. There are 20 "25"s in 501, (20 x 25 = 500), so a D地i ?0?digit goes in the 25s place

2. There's a remainder of 501 - 500 = 1, so 1 will go in the 1s place. 

In summary 9,876 = (15 x 625) + (20 x 25) + 1.

15625s

625s

25s

1s

0

15

20

1

 

%

)

1

 So, 9,876 in D地i consists of the digits for 15, 20, and 1, or %  )  1

 

Here痴 another example, converting 297,056 to D地i, We will start at the power 3 column, since 15,626 < 297,056. We first divide 297,056 by 15,625, the place value for power column 3. The result, 19.011584, tells us:

1. There are 19 "15,625"s in 297,056, (19 x 15,625 = 296,875), so a D地i ?9? digit goes in the 15,625s place.
2. There's a remainder of 297,056 - 296,875 = 181.

So far 297,056 = (19 x 15,625) + 181. We next need to determine the digit for the 625s place.

But 625 is not less than 181. Said another way, there are no 625s in 181. So the 625s place gets a 0:
297,056 = (19 x 15,625) + (0 x 625) + 181.

Move right to the 25s column and continue the calculation using 181. Divide 181 by 25 (=7.24).

1. There are 7 "25"s in 181, (7x25=175), so a D地i ??digit goes in the 25s place.
2. There's a remainder of 181-175=6, so 6 will go in the 1s place.

In summary 297,056 = (19 x 15,625) + (0 x 625) + (7 x 25) + 6.

15625s

625s

25s

1s

19

0

7

6

(

:

7

6

So, 297,056 in D地i is (  :  7  6

May 13, 2004