Let $\Sigma=\{0,1\}$ and $L=\{u \in \Sigma^* : u \text{ has odd number of 0's and odd number of 1's}\}$. How can I build a regular expression or an automaton for this language? I have no idea, and I guess $L$ is not regular, but I haven't been able to prove it with the pumping lemma.
If it is not regular, can you give me a hint to prove it?