**Ok, here we go**
Ok folks I think I found what I was looking for.

The trandponders are based on the "octal" notation system. Basically, octal notation is composed of three-bit groups (Just like pink Panther showed, except he left out 0= 0 0 0). Thus you can only go from 0-7 (eight numbers)

Because there are only 8 numbers to play with...8 to the 4th power is 4096.

If you tried to represent all the possible codes without octal, straight binary, going up to 10 total numbers (0-9) you would end up with something like 14 bits for every transmission. Even simply using 0-7 with straight binary gives you 13 bits.

Using octal (0-7) you can send out all possible codes with only 12 bits. If you move up to hexidecimal (0-15) you would be sending 16 bits in each transmission.

So, out of all of those, octal is the most efficient for a system with 4 separate numbers to be used.

Confused?

Skeezer