## We strongly recommend that you click here and practice it, before moving on to the solution.

**1. **A simple method for this is to simply take the log of the number on base 2 and if you get an integer then number is power of 2.

**2. **Another solution is to keep dividing the number by two, i.e, do n = n/2 iteratively. In any iteration, if n%2 becomes non-zero and n is not 1 then n is not a power of 2. If n becomes 1 then it is a power of 2.

#include<stdio.h> #define bool int /* Function to check if x is power of 2*/ bool isPowerOfTwo(int n) { if (n == 0) return 0; while (n != 1) { if (n%2 != 0) return 0; n = n/2; } return 1; } /*Driver program to test above function*/ int main() { isPowerOfTwo(31)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(17)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(16)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(2)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(18)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(1)? printf("Yes\n"): printf("No\n"); return 0; }

Output:

No No Yes Yes No Yes

**3. **All power of two numbers have only one bit set. So count the no. of set bits and if you get 1 then number is a power of 2. Please see http://geeksforgeeks.org/?p=1176 for counting set bits.

**4. ** If we subtract a power of 2 numbers by 1 then all unset bits after the only set bit become set; and the set bit become unset.

For example for 4 ( 100) and 16(10000), we get following after subtracting 1

3 –> 011

15 –> 01111

So, if a number n is a power of 2 then bitwise & of n and n-1 will be zero. We can say n is a power of 2 or not based on value of n&(n-1). The expression n&(n-1) will not work when n is 0. To handle this case also, our expression will become n& (!n&(n-1)) (thanks to Mohammad for adding this case).

Below is the implementation of this method.

#include<stdio.h> #define bool int /* Function to check if x is power of 2*/ bool isPowerOfTwo (int x) { /* First x in the below expression is for the case when x is 0 */ return x && (!(x&(x-1))); } /*Driver program to test above function*/ int main() { isPowerOfTwo(31)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(17)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(16)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(2)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(18)? printf("Yes\n"): printf("No\n"); isPowerOfTwo(1)? printf("Yes\n"): printf("No\n"); return 0; }

Output:

No No Yes Yes No Yes

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