# Find whether a given number is a power of 4 or not

Find whether a given number is a power of 4 or not - Bit Algorithm - A simple method is to take log of the given number on base 4, and if we get an integer.

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

1. A simple method is to take log of the given number on base 4, and if we get an integer then number is power of 4.

2. Another solution is to keep dividing the number by 4, i.e, do n = n/4 iteratively. In any iteration, if n%4 becomes non-zero and n is not 1 then n is not a power of 4, otherwise n is a power of 4.

c
``````#include<stdio.h>
#define bool int

/* Function to check if x is power of 4*/
bool isPowerOfFour(int n)
{
if(n == 0)
return 0;
while(n != 1)
{
if(n%4 != 0)
return 0;
n = n/4;
}
return 1;
}

/*Driver program to test above function*/
int main()
{
int test_no = 64;
if(isPowerOfFour(test_no))
printf("%d is a power of 4", test_no);
else
printf("%d is not a power of 4", test_no);
getchar();
}``````

3. A number n is a power of 4 if following conditions are met.
a) There is only one bit set in the binary representation of n (or n is a power of 2)
b) The count of zero bits before the (only) set bit is even.

For example: 16 (10000) is power of 4 because there is only one bit set and count of 0s before the set bit is 4 which is even.

Thanks to Geek4u for suggesting the approach and providing the code.

c
``````#include<stdio.h>
#define bool int

bool isPowerOfFour(unsigned int n)
{
int count = 0;

/*Check if there is only one bit set in n*/
if ( n && !(n&(n-1)) )
{
/* count 0 bits before set bit */
while(n > 1)
{
n  >>= 1;
count += 1;
}

/*If count is even then return true else false*/
return (count%2 == 0)? 1 :0;
}

/* If there are more than 1 bit set
then n is not a power of 4*/
return 0;
}

/*Driver program to test above function*/
int main()
{
int test_no = 64;
if(isPowerOfFour(test_no))
printf("%d is a power of 4", test_no);
else
printf("%d is not a power of 4", test_no);
getchar();
}``````
See also  Program to count number of set bits in an (big) array 