Find position of a number in binary number?

Question

I know that 1024 is at the 10th position in a binary number : 2^10 = 1024. However, if I take the problem on the other side, at which position is 1024. How I can know that?

Answer 1

If you are asking, "What is the highest bit set to 1 in a binary number given a number in base 10?", then you can do it this way:

‪‪‪‪‪‪‪‫‪‪b = ceil(log_2(n))

ceil() is the ceiling function: http://en.wikipedia.org/wiki/Ceiling_function
log_2() is logarithm base 2: http://en.wikipedia.org/wiki/Logarithm

In your example,

b = ceil(log_2(1024)) = ceil(log_10(1024)/log_10(2)) = 10

Answer 2

If the given number is is b you must solve
2^x=b so
x= ln(b)/ln(2)