How to perform multiplication, using bitwise operators?

Question

I am working through a problem which i was able to solve, all but for the last piece - i am not sure how can one do multiplication using bitwise operators:

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Answer 1

To multiply two binary encoded numbers without a multiply instruction. It would be simple to iteratively add to reach the product.

unsigned int mult(x, y)
unsigned int x, y;
{
    unsigned int reg = 0;

    while(y--)
        reg += x;
    return reg;
}

Using bit operations, the characteristic of the data encoding can be exploited. As explained previously, a bit shift is the same as multiply by two. Using this an adder can be used on the powers of two.

// multiply two numbers with bit operations

unsigned int mult(x, y)
unsigned int x, y;
{
    unsigned int reg = 0;

    while (y != 0)
    {
        if (y & 1)
        {
            reg += x;
        }
        x <<= 1;
        y >>= 1;
    }
    return reg;
}