Could you please explain how did you convert such a huge number from base 8 to base 10? I can see that conversion from one base to the other when both of them are some integral powers of 2 is easy. But what about a base which is not anintegral power of 2. Is there a general approach that could be followed while converting between arbitrary bases?

:o)
Regards,
Deep G

As to the implementation, Java has a class BigInteger that accepts strings of arbitrary length. So in Java, it was pretty simple:

BigInteger bi = new BigInteger(yourNumberString, 8); // octal system
print(bi.toString(10)); // decimal system

Now, this probably won't satisfy your curiosity. For, the explanation begs a question, "And how the class BigInteger has been implemented?"

Well, I do not know the details, but can imagine a possibility of having a sequence of integers where each member is considered as a "big digit". For example, you can store numbers in triples of digits. Say, 1234567770 could be stored as

770 + 567·10³ + 234·10⁶ + 1·10⁹, or as, say,

(1, 9), (234, 6), (567, 3), (770, 0)

Multiplication and division over such explicit'sequences can certainly can be devised, although, again, the implementation may be tedious.

N 35° 08.837 W 089° 59.569

The latitude, in the degrees and decimal arcminutes format you have mentioned, will need to represent numbers up to 180 degrees, which will require 8 binary digits (since 2^8 is the first power of 2 which is larger than 180), and upto 59.999 minutes, which will require 16 binary digits (since 2^16 = 65536 is the first power of 2 which is larger than 59,999). Altogether the numbers will require 24 digits, and at least one extra digit to represent N or S. The longitude coordinate is similar. Therefore, each coordinate pair will require a minimum of 50 binary digits, and perhaps more if there are some start and stop code numbers. Since 3 binary digits is one base 8 digit, this means that each coordinate pair must be at least 13 digits long. Its actual length may be longer if there are any "filler numbers."

Then, within each shorter message, look for key number combinations that probably represent N S E and W. These would be expected to be in similar positions within each message, and in each position, there should only be two values, representing N or S in the first postion, and E or W in the second. Also, it is possible that the number values will be signed, with plus representing N and E, and minus representing S and W. The representation of signed numbers can be done with either sign/magnitude or with 2's complement format, which requires converting the base 8 digits into binary. Either of these formats will start with a binary digit 1 if negative and 0 if positive. A base 8 digit "7" represents three 1's in a row, and so is likely (but not certain) to be the start of a negative number.

This is basically a lesson in codebreaking, since you don't have direct knowledge of how the geographical coordinates are encoded in the number string. The best thing to do, of course, is to simply ask the person responsible for the number string what the encoding is, but I assume you can't do that, or you wouldn't be asking here. There is much more to codebreaking than what I have said here, and much more in fact that I do not know (I'm only an amateur). One thing I do know is that codebreaking can be a LOT of work! And you're never really sure you've got it right until you can try your decoding method on a fresh number string from the same source.

Hope this helps,

--Stuart Anderson