$1.$Non$-$negative binary integers divisible by $4($decimal$)[100($binary$)]$: Consider the

binary representation of non$-$negative integers that are divisible by $4.$ These numbers

have the following properties:

a$.$ The number zero $(0)$ is included.

b$.$ All non$-$zero integers must end with the binary digits $00.$

c$.$ For this problem: All non$-$zero integers must start with the digit $1($no leading $0\text{'}$s$,$

except for the number zero itself$).$

Since the problem involves binary numbers, the relevant alphabet is $=\{0,1\},$

d$.$ Write a DFA with no more than $12$ states that accepts exactly these non$-$negative

binary integers that are divisible by $4.$

b$.$ Write an NFA with no more than $8$ states that accepts exactly these integers. $($For

this part, the NFA must not also be a DFA.$)$

For each automaton, be sure all transitions are clearly identified and all states are clearly

specified as accepting or not.