$1.$ Design a DFA that accepts all unsigned binary integers that are less than $8.$

Examples: $11,00001,101,...$

$2.$ Design a DFA that accepts all positive decimal integers divisible by $3.$

Examples: $03,12,33,999,$

$3.$ Let G be a grammar with the start variable S and the following productions:

S $->$ aA $|\backslash$lambda

A $->$ bbS

i$)$ Give a simple description of the language L$($G$)$ generated by grammar G above.

ii$)$ Show a derivation of the string w $=$ abbabb from G$.$

iii$)$ Suppose L $=\{$w : w in L$($G$)$ and $|$w$|<=10\}.$ What is L

R$,$ the reverse of L$?$

PLEASE ACTUALLY DRAW ALL THE DIAGRAMS PROPERLY IN DFA FORMAT