Find a DFA for the following language on Σ = {0, 1}
L = {w : the value of w, interpreted as a binary representation of an integer is zero modulo five}. For example, 0101 and 1111, representing the integers 5 and 15, respectively, are to be accepted. Hint: Label the states with the value (mod 5) of the partial bit string. To take care of the next bit, use the relationship 2n mod 5 = (2n mod 5) mod 5, (2n + 1) mod 5 = [(2n mod 5) + 1] mod 5.
