Find the result of a function - recursion

Question

There is a code of an unknown function:
function Magic(number)
r = number mod 2
print r
if number > 1
Magic(number / 2)
(written in pseudo-code)
The question is: what integer number should be passed in order to receive the following answer
0 1 1 0 0 1
The main problem is that I can't figure out how mod is working in pseudocode.
Should 5,5 mod 3 = 2.5 or 2

Answer 1

Both division and mod operations are only supposed to accept and output integer numbers here. "5.5 mod 3" f.e. doesn't really make any sense. And 11 / 2 (integer division) will return 5, not 5.5.
Here's a PHP program that implements your pseudo code:
<?php
function Magic($number) {
$r = $number % 2;
echo $r . ' ';
if ($number > 1) Magic($number / 2);
}
for ($i = 16; $i < 34; ++$i) {
echo "($i: ";
Magic($i);
echo ") ";
}
echo "\n";
Results in output:
(16: 0 0 0 0 1 ) (17: 1 0 0 0 1 0 ) (18: 0 1 0 0 1 0 ) (19: 1 1 0 0 1 0 ) (20: 0 0 1 0 1 0 ) (21: 1 0 1 0 1 0 ) (22: 0 1 1 0 1 0 ) (23: 1 1 1 0 1 0 ) (24: 0 0 0 1 1 0 ) (25: 1 0 0 1 1 0 ) (26: 0 1 0 1 1 0 ) (27: 1 1 0 1 1 0 ) (28: 0 0 1 1 1 0 ) (29: 1 0 1 1 1 0 ) (30: 0 1 1 1 1 0 ) (31: 1 1 1 1 1 0 ) (32: 0 0 0 0 0 1 ) (33: 1 0 0 0 0 1 0 )
Which shows that the 6-digit result (x: 0 1 1 0 0 1 ) is impossible for any integer x (because of the monotonic growth of the output string). However, Magic(38) is 0 1 1 0 0 1 0 — the first 7-digit result with your required string, but also having a trailing zero.
As for the negative integer values, the only 2 outputs possible are "0 ", and "-1 ".

Answer 2

First of all, here is executable python code for this problem.
def Magic(number):
r = number % 2
print r
if number > 1:
Magic(number / 2)
Magic(15)
However, the pattern in this problem is that the function is returning the REVERSE binary number for the given input number. So, in this instance, the easiest solution would be to take 0 1 1 0 0 1, reverse it to 100110, and calculate the value of that binary number, which is 32 + 4 + 2 = 38. Using this methodology, you can calculate the required number or the expected output for any given input.

Answer 3

mod gives you the remainder of a integer division. A few examples:
1 mod 2 = 1 (since 1 / 2 = 0 in integer division)
2 mod 2 = 0 (2 / 2 = 1, no remainder)
6 mod 3 = 0 (6 / 3 = 2, no remainder)
8 mod 3 = 2
The fraction part should probably be left out. in most languages it depends on the datatype of the number (some languages do integer division if both operands are integers, and this is probably what you should do too, so 5/2 = 2).
As to your first question (spoiler alert!, try it yourself before reading this!), begin from the end and multiply by two in every step. Also add 1 if the number should be 1 in that step.
So, the last step is a 1. Begin with 1:
1
1*2 = 2
2*2 = 4
4*2+1 = 9
and so on. I could give you the correct answer but I think it's better if you try it yourself ;-)