How Can a Finite State Machine Validate a Language Based on Bitwise Addition?

[MalickT]

I have alphabeth {000, 001, 010, 011, 100, 101, 110, 111}
There is a langugage L. Strings that belong in this langugage only when 1-st bitrow + 2nd bitrow = 3-rd bitrow
For example: a 3 letter word "001100110" belongs in the language cause if to look them in rows:

011
001
100

011 + 001 = 100

Even one letter word "000" belongs in the language cause:

0
0
0

0 + 0 = 0

I hope u get the picture. PS! language L contains 1 to million (or more) letter words. How do I do a Finate State Machine which accepts strings that belong in the langugage? My teacher said it not that hard but i just don't know how to start...Please help!

 

[daniel_i_l]

I don't see what a FSM has anything to do with this. Let's say you want to check if string A is in the language. Just subtract each letter in the alphabet from A and see if you get another letter.

 

[MalickT]

Can u expalin more detailed? I don't know, my assaingment says i have to pruve that this langugage is regular by makeing a FSM