The DFA for even numbers of and b is this DFA for even numbers of a and b but the DFA of even and equal number of a and b is not available L={\epsilon,aabb,abab,baba,bbaa,aaaabbbb,aabbaabb,bbaabbaa,babababa,abababab,bbbbaaaa,........}
i am new to toc so guide me with easy answer please
You can design a DFA for a given language only if that language is regular. The language you described above is not a regular language. Therefore, you cannot design a DFA (or NFA or regular expression) for it.
The proof of non-regularity of the above language is by the use of the famous pumping lemma (for regular languages): Assume to the contrary that the language, call it L, is regular. Let p be the pumping length given by the pumping lemma. Let s be the string a^{2p}b^{2p}. Because this string is a member of L and it has length more than p, the pumping lemma guarantees that it can be split into three pieces, s = xyz, satisfying the three conditions of the lemma; But this outcome is in fact impossible: Piece y is made only of a's, say y=a^k (k >= 1). So, xz = xy^0z = a^{2p-k}b^p is not in L.