What is the logic of this C++ Loop that converts Decimal to Binary

Question

I am searching for codes that converts decimal to binary and i stumbled upon this:

#include <iostream>

using namespace std;


int main()
{
    int num;
    cout << "Please enter a number: ";
    cin >> num;
   
    if (num > 0) {
      int i = 1;
      while (i <= num)
      i *= 2;
      i /= 2;

      do {
        if (num >= i) {
           cout << '1';
           num -= i;
        }
        else
           cout << '0';
        i /= 2;
      } while (i > 0);
      cout << "";
      
    }
    
    else
      cout << '0';
}

I can't seem understand the logic of this loop

 while (i <= num)
      i *= 2;
      i /= 2;

i tried to put cout in between the equations to see the process

 while (i <= num)
    cout << i;
    cout << "A";
      i *= 2;
    cout << i;
    cout << "B";
      i /= 2;
    cout << i;
    cout << "C";

but it results to 111111111111111111... and doesn't stop can someone please explain

Answer 1

When working to understand any algorithm, you step through it with pencil-and-paper validating each step of the code. Pick a small test case, such as 10 as your input, which you know has a binary representation of 1010 and step through the four-iterations understanding what is happening.

If you do so, you will find the following:

    while (i <= num)            /* find next power-of-two greater than num */
        i *= 2;

and then it is reduced by a power-of-two to eliminate any leading zeros as output, e.g.

    i /= 2;                     /* divide by two, 1st power-of-two less than num */

This ensures i is the next power-of-two less than num. Now look at the algorithm in the do .. while (i > 0); loop (rearranged and indented so it makes more sense):

    do {                        /* loop until i <= 0 */
        if (num >= i) {         /* is num >= i? */
            std::cout << '1';   /* if so, output character '1' */
            num -= i;           /* reduce num by i */
        }
        else    /* otherwise */
            std::cout << '0';   /* output '0' character if num < i */
        i /= 2;                 /* divide i by 2 (integer division intentional) */
    } while (i > 0);

The algorithm is simple.

1. Iteration one - since i is the next power-of-two less than num the conditional if (num >= i) will test true guaranteeing the first character output will be '1'. num is then reduced by i (in the case where num = 10;), i = 8 on the first iteration so num -= i; leaves num = 2. i is divided by 2 leaving i = 4.
2. Iteration two - the conditional is false, '0' is output and i is divided again by 2 leaving i = 2, so i = num = 2.
3. Third iteration - the conditional tests true, the character '1' is output, num is reduced to 0, i is reduced to 1, you loop again.
4. Fourth iteration - the conditional is false, '0' is output and i is reduced to zero exiting the loop.

The correct binary representation of 10 is output:

1010

If you refactor the code to eliminate the unnecessary else condition based on whether num >= 0, you simply handle the negative or zero case and return. That saves a complete level of indention throughout the code. Putting it altogether, you can rewrite the same code as:

#include <iostream>

int main()
{
    int num, i = 1;
    std::cout << "Please enter a number: ";
    std::cin >> num;
    
    if (num <= 0) {
        std::cout << "0\n";
        return 0;
    }
    
    while (i <= num)            /* find next power-of-two greater than num */
        i *= 2;
    
    i /= 2;                     /* divide by two, 1st power-of-two less than num */

    do {                        /* loop until i <= 0 */
        if (num >= i) {         /* is num >= i? */
            std::cout << '1';   /* if so, output character '1' */
            num -= i;           /* reduce num by i */
        }
        else    /* otherwise */
            std::cout << '0';   /* output '0' character if num < i */
        i /= 2;                 /* divide i by 2 (integer division intentional) */
    } while (i > 0);
    
    std::cout << '\n';          /* tidy up with newline */
}

(note: See Why is “using namespace std;” considered bad practice? -- learning good habits is much easier than breaking bad ones later....)

Example Use/Output

$ ./bin/binary_conversion
Please enter a number: 10
1010

or

$ ./bin/binary_conversion
Please enter a number: 126
1111110

or

$ ./bin/binary_conversion
Please enter a number: 170
10101010

The code works fine. Look things over and let me know if you have further questions.

Answer 2

C++ is not Python, indentation and format literally has no effect.

 while (i <= num)
      i *= 2;
      i /= 2;

equals to

 while (i <= num)
 {
      i *= 2;
 }
 i /= 2;

That is, if while is not followed by a compound statement (i.e. statement block, surrounded by a pair of {}), then the loop body is only the first statement following while.

Latest version of commonly used compilers should have reported a warning about misleading indentation, it is a good habit to read every warning carefully.