Construct DFA, RE$,$ CFG and convert it into CNF for the following:

a$.$ Binary strings ending with $00.$

b$.$ Binary strings beginning with $0$ and ending with $1.$

c$.$ Binary strings containing two consecutive $0$s$.$

d$.$ Binary strings containing $000$ as substring.

e$.$ Binary strings containing at least one $0.$

f$.$ Binary strings beginning and ending with a $0.$

g$.$ Strings made up of the symbols $\{$a$,$b$\}$ that has at most one b$.$

h$.$ Binary strings that begin with $0$s followed by $1$s which in turn follwoed by $0$s$.$

i$.$ Binarystrings begin and end with a $1$ and where there is exactly one $0$ between

each $1.$