Please write this in pseudocode

Problem 3. (30p) Given a positive integer n, consider the algorithm that finds the number of digits in its binary representation. Example: 8 = 10002 - 4 digits ; 7 = 1112 - 3 digits 3.1 (7) Write a recursive version of this algorithm 3.2 (10p) Prove correctness of the recursive solution using induction. Clearly state the claim, base case and the induction step 3.3 (8p) Write a non-recursive solution that uses loops. 3.4 (5p) Identify the loop invariant of the non-recursive algorithm. Remember that the loop invariant LI = the "thing that always holds whenever the loop executes. Should be informative such that proving the correctness of the LI leads to the correction of the whole algorithm