ALGORITHM 1

Input: a positive integer n
Output: a sequence of bits representing the number in binary.
For an input of n = 11, the output should be (1, 0, 1, 1).

Step 0: start with an empty output sequence S = ()
Step 1: if n is 0,  return the sequence S.
Step 2: divide n by 2 to get k with remainder r; r must be 0 or 1.
Step 3: prepend r onto S. replace n with k.
Step 4: go to step 1.

ALGORITHM 2

Input: a positive integer n
Output: a sequence of bits representing the number in binary.
For an input of n = 11, the output should be (1, 0, 1, 1).

Step 0: start with an empty output sequence S = ()
Step 1: divide n by 2 to get k with remainder r; r must be 0 or 1.
Step 2: prepend r onto S. replace n with k.
Step 3: if n is 1,  return the sequence S.
Step 4: go to step 1.