Minimum number of bits to represent number

Question

What is the most efficient way to find out how many bits are needed to represent some random int number? For example number 30,000 is represented binary with

111010100110000

So it needs 15 bits

Answer 1

You may try:

Math.Floor(Math.Log(30000, 2)) + 1

or

(int) Math.Log(30000, 2) + 1

Answer 2

int v = 30000; // 32-bit word to find the log base 2 of
int r = 0; // r will be lg(v)

while ( (v >>= 1) != 0) // unroll for more speed...
{
  r++;
}

For more advanced methods, see here http://graphics.stanford.edu/~seander/bithacks.html#IntegerLogObvious

Note that this computes the index of the leftmost set bit (14 for 30000). If you want the number of bits, just add 1.

Answer 3

Try log(number)/log(2). Then round it up to the next whole number.