$3.$ Work out the following problems from first principles without converting to binary and counting the bits. Then compare with the formulae presented for encoding a character string into an integer, and vice$-$versa, in the specified radix. $($Hint: Consider the next$-$lower and next$-$higher power of two for each integer.$)$

a$)$ How many bits are exactly required to encode the following integers? $($The number shown as an integer$$s subscript refers to the radix of that integer.$)$

b$)$Exactly how many bytes are required to represent the numbers in $($a$)$ above?