How can I perform multiplication without the '*' operator?

Question

I was just going through some basic stuff as I am learning C. I came upon a question to multiply a number by 7 without using the * operator. Basically it\'s like this

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Answer 1

O(log(b)) method

public int multiply_optimal(int a, int b) {

    if (a == 0 || b == 0)
        return 0;
    if (b == 1)
        return a;
    if ((b & 1) == 0)
        return multiply_optimal(a + a, b >> 1);
    else
        return a + multiply_optimal(a + a, b >> 1);

}

The resursive code works as follows:
Base case:
if either of the number is 0 ,product is 0.
if b=1, product =a.

If b is even:
ab can be written as 2a(b/2)
2a(b/2)=(a+a)(b/2)=(a+a)(b>>1) where'>>' arithematic right shift operator in java.

If b is odd:
ab can be written as a+a(b-1)
a+a(b-1)=a+2a(b-1)/2=a+(a+a)(b-1)/2=a+(a+a)((b-1)>>1)
Since b is odd (b-1)/2=b/2=b>>1
So ab=a+(2a*(b>>1))
NOTE:each recursive call b is halved => O(log(b))