How not to print zeros at the beginning of the binary representation of a usigned short int?

Question

I have a code like this that converts a short integer to binary, but zeros are printed at the beginning. So here's how to make sure that these zeros are not displayed, and the output starts from the first one? At the same time, using standard language operators and bitwise operations.

int main()
{
    unsigned short int k;
    
    while (true)
    {
        cin >> k;
        if (!k)
        {
            break;
        }
        for (int i = 0; i < 16; i++)
        {
            cout << (k >> 15);
            k <<= 1;
        }
        cout << endl;
    } 

Answer 1

With recursion, you might do:

void print_binary(unsigned int n)
{
    if (n >> 1 != 0) print_binary(n >> 1);
    std::cout << (n & 1);
}

Demo