Binary math

Question

If I know the number number y and know that 2^x=y, how do I compute x?

Answer 1

Base 2 logarithm function:

log2(y)

which is equivalent to:

log(y) / log(2)

for arbitrary base.

Answer 2

If you are sure that it is a power of 2, then you can write a loop and right shift the number until you get a 1. The number of times the loop ran will be the value of x.

Example code:

int power(int num)
{
    if(0 == num)
    {
     return 0;
    }

    int count = 0;
    do
    {
     ++count;
     num = num >> 1;
    }while(! (num & 1) && num > 0);
    return count;
}

Answer 3

And in case you don't have a log function handy, you can always see how many times you must divide y by 2 before it becomes 1. (This assumes x is positive and an integer.)

Answer 4

If x is a positive integer, then, following code will be more efficient..

   unsigned int y; // You know the number y for which you require x..
   unsigned int x = 0; 

   while (y >>= 1) 
   {
         x++;
   }

x is the answer!