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

Thanks in advance

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- Apr 25th 2008, 12:46 AMfarakhkhan@yahoo.comFinite 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?

Thanks in advance

- Apr 25th 2008, 07:03 AMAlvyda
What is FA?

- Apr 25th 2008, 08:52 AMIsomorphism
Hint:Let the binary number 'x' have k ones in it. Then $\displaystyle x = \sum_{j=1}^{ j=k} 2^{i_j}$.

But modulo 3 this reads:

$\displaystyle x \, mod 3 = \sum_{j=1}^{ j=k} (-1)^{i_j}$.

However we want this to be 0 mod 3. Then can you figure out the constraint on $\displaystyle i_j$s?

Quote:

Originally Posted by**Alvyda**