What's wrong with my answer?(Finite Automata)

Question

Quite confused with this problem here regarding finite automata

Consider the finite automaton

M=({q0,q1}, {0}, {((q0,0),q1), ((q1,0),q0)}, q0, {q1}). 

If the alphabet is {0,1} , what happens to the machine if the input string contains 1? Modify the FA so that the problem is resolved.

I tried to change the transition function ((q0, 0),q1)) into ((q0,1),q1)) , which from my understanding would make the finite automata correct. Professor says its still wrong. Any help with this?

Answer 1

As of now your automata accepts strings that has an odd number of zeroes. because 2 0's will take you back to the same start state again and q_1 is only on 0 away from q_0. But this dfa still remains incomplete, as there is no mapping for delta (q_0,1), delta(q_1,1) So, in-case you encounter a 1, you need to clearly stay in the same place, ie q0 or q1 since this does not change the number of 0's you have seen up until then