Problem $1$

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

Construct NFAs that recognize the following languages:

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

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

All binary numbers that contain $00$ or $11.$

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 show all work and steps please.