Draw $($and include in the PDF you submit to Gradescope$)$ state diagrams of DFAs with as few

states as you can recognizing the following languages. You may assume that the alphabet in each

case is $=\{0,1\}.$

$($a$)L_1=\{\begin{array}{c}w|w\end{array}$ is a string of the form $x_1{y}_1{x}_2{y}_{2}dots{x}_n{y}_n$ for some natural number $n$ such that

if $x$ is the integer with binary representation $x_1{x}_{2}dots{x}_n$ and if $y$ is the integer with binary

representation $y_1{y}_{2}dots{y}_n,$ then $xy$