Build deterministic finite automata for each the following language.

The set of all strings beginning with a 1 such that, interpreted as a binary representation of an integer, it has a remainder of 1 when divided by 3.

For example, the binary number 1010b is decimal 10. When you divide 10 by 3 you get a remainder of 1, so 1010 is in the language. However, the binary number 1111b is decimal 15. When you divide 15 by 3 you get a remainder of 0, so 1111 is not in the language.