Problem $4$

Converting decimal numbers to binary numbers can be done recursively. Write a

function that takes a positive int argument and returns the corresponding binary

number as an int composed of only ones and zeros. For example, convert$(5)$

returns the int: $101.$

The insight for this problem comes from the fact that the rightmost digit of a

decimal $n$ is easy to calculate. It is the remainder when dividing by the base $2$ :

$n\%2.$ To get the next rightmost digit, you take the resulting quotient, that is$,$

$n2=\frac{n}{2},$ and find its remainder, $n2\%2,$ which is the next digit. Unfortunately,

that generates the digits from right to left and we want them from left to right.

We could easily do that non$-$recursively using string concatenation or string

reversal, but in this exercise you are to use recur$-$ sion to recursively calculate

the digits. Effectively, you are letting recursion reverse the ordering: think in

terms of calculating the rightmost digit as described previously, but then let

recursion reverse the digits.