# Math Help - Finite Automata Question

1. ## Finite Automata Question

How can I draw FA over {0, 1} which represent binaries of Integers only divisible by 3 and all leading 0’s are permissible?

2. What is FA?

3. Originally Posted by farakhkhan@yahoo.com
How can I draw FA over {0, 1} which represent binaries of Integers only divisible by 3 and all leading 0’s are permissible?

Hint:Let the binary number 'x' have k ones in it. Then $x = \sum_{j=1}^{ j=k} 2^{i_j}$.
$x \, mod 3 = \sum_{j=1}^{ j=k} (-1)^{i_j}$.
However we want this to be 0 mod 3. Then can you figure out the constraint on $i_j$s?