It's a method that works like this: We represent any number representation in a base with vectors like this: X*100+Y*10+Z -> (X,Y,Z) (the below vectors for example are symbols for representations in the base 2) (0,0,1)
(0,1,1)
(0,1,10BIN=2)
Now we've got to convert that into something that can be converted in binary, so with this case you would do this:
(0,1+1,0+0)
(0,10BIN,0+0)
(1+0,0+0,0)
(1,0,0)
Conclusion: 1+11BIN=100BIN
Immplementation 2 is more optimized, instead of dectecting change, it sees if what is in all of the digit plaaces is legal