$4.(16$ pts$)$ Each of the following languages is the intersection of two simpler languages. In each part, first identify the two simpler languages, and construct a state diagram of a DFA for the language given. Then combine the two state digrams to give a DFA state diagram for the combined language. In all parts, $\backslash$Sigma $=\{0,1\}.$

a$)\{$w$|$w has an even number of $0$s and one or two $1$s$\}$

b$)\{$w$|$w has an odd number of $0$s$,$ and ends with a $1\}$