Draw the state diagrams by hand dont use Chat Gpt $.$ Also answer both the problems since they are interlinked $.$

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.