Good, so you need to consider for zero cases where there are odd and even. This requires two states: one for even zeros, one for odd zeros. Then for the case with an odd zero, you need to have 1 one, and then an even number of units. For an even case, you just need an even number.
It's easy to write DFA, but I don't know how to do this, so I'm going to question the regex:
(0 (00)* 1 (11)*) \/ (00)*(11)*
Il-bhima
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