Problem 1 Total: 30 points (10 points each)

Construct NFAs that recognizes the following languages:

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

2. All binary numbers that contain at most two 1s or contain at most two 0s (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.