Need help on Theory of Computation:

3. You probably know the trick that a number is a multiple of 9 if and only if the sum of its of ), Here is a similar tick for decimal digits is a multiple of 9. Here is a similar trick for multiples of 3 in binary. Ptowe that a mumber is a multiple of s if and only if writing that number backwards in binary is also a multiple of 3. Example: 0011 bin-3dec s a multiple of 3, and so is 11 00bin-12dec. However, 100101 bin- 7dec is not a multiple of 3, and neither is 101001 bin-41dec. Hint: First transform this to a statement about regular languages over alphabet (0, 1)