Problem

In this question, the function INT($X$) is the largest integer less than or equal to $X$. For example, INT(5.7) = 5, INT(8) = 8, INT(−2.3) = −3.

Consider the following algorithm.

Step 1: Input $N$

Step 2: Calculate $A = N \div 10$

Step 3: Let $B$ = INT($A$)

Step 4: Calculate $C = B \times 10$

Step 5: Calculate $D = N - C$

Step 6: Output $D$

Step 7: Replace $N$ by $B$

Step 8: If $N = 0$ then STOP, otherwise go back to Step 2

(a) Complete the table in the answer book, using $N = 4217$, to show the results obtained at each step of the algorithm.

(b) Explain how the output values of the algorithm relate to the original input $N$, where $N$ is any positive integer.