Total: $30$ points $(10$ points each$)$

Construct NFAs that recognizes the following languages:

$1.$ All binary numbers that contain a $1$ in the $3$rd location from the right $($e$.$g$.100,10111,...)$

$2.$ All binary numbers that contain at most two $1$s or contain at most two $0$s $($e$.$g$.,111101,01000,...)$

$3.$ All binary numbers that can be divided by $4.$

Problem $2$

Total: $30$ points

Via subset construction, construct DFAs from all three NFAs that were constructed in problem $1.$ You must

show the transition tables of the DFAs you construct and their state diagram.

Please answer both the questions since they are interlinked and draw the state diagrams by hand $.$