# Python Program to find whether a no is power of two

Given a positive integer, write a function to find if it is a power of two or not.**Examples :**

Input : n = 4 Output : Yes 2^{2}= 4 Input : n = 7 Output : No Input : n = 32 Output : Yes 2^{5}= 32

**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.

## Python3

`# Python3 Program to find` `# whether a no is` `# power of two` `import` `math` `# Function to check` `# Log base 2` `def` `Log2(x):` ` ` `return` `(math.log10(x) ` `/` ` ` `math.log10(` `2` `));` `# Function to check` `# if x is power of 2` `def` `isPowerOfTwo(n):` ` ` `return` `(math.ceil(Log2(n)) ` `=` `=` `math.floor(Log2(n)));` `# Driver Code` `if` `(isPowerOfTwo(` `31` `)):` ` ` `print` `(` `"Yes"` `);` `else` `:` ` ` `print` `(` `"No"` `);` `if` `(isPowerOfTwo(` `64` `)):` ` ` `print` `(` `"Yes"` `);` `else` `:` ` ` `print` `(` `"No"` `);` ` ` `# This code is contributed` `# by mits` |

**Output:**

No Yes

**Time Complexity: **O(log_{2}n)

**Auxiliary Space: **O(1)

**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.

## Python3

`# Python program to check if given` `# number is power of 2 or not` `# Function to check if x is power of 2` `def` `isPowerOfTwo(n):` ` ` `if` `(n ` `=` `=` `0` `):` ` ` `return` `False` ` ` `while` `(n !` `=` `1` `):` ` ` `if` `(n ` `%` `2` `!` `=` `0` `):` ` ` `return` `False` ` ` `n ` `=` `n ` `/` `/` `2` ` ` ` ` `return` `True` `# Driver code` `if` `(isPowerOfTwo(` `31` `)):` ` ` `print` `(` `'Yes'` `)` `else` `:` ` ` `print` `(` `'No'` `)` `if` `(isPowerOfTwo(` `64` `)):` ` ` `print` `(` `'Yes'` `)` `else` `:` ` ` `print` `(` `'No'` `)` `# This code is contributed by Danish Raza` |

**Output:**

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 Count set bits in an integer 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 https://www.geeksforgeeks.org/program-to-find-whether-a-no-is-power-of-two/Mohammad for adding this case).

Below is the implementation of this method.

## Python3

`# Python program to check if given` `# number is power of 2 or not` `# Function to check if x is power of 2` `def` `isPowerOfTwo (x):` ` ` `# First x in the below expression` ` ` `# is for the case when x is 0` ` ` `return` `(x ` `and` `(` `not` `(x & (x ` `-` `1` `))) )` `# Driver code` `if` `(isPowerOfTwo(` `31` `)):` ` ` `print` `(` `'Yes'` `)` `else` `:` ` ` `print` `(` `'No'` `)` ` ` `if` `(isPowerOfTwo(` `64` `)):` ` ` `print` `(` `'Yes'` `)` `else` `:` ` ` `print` `(` `'No'` `)` ` ` `# This code is contributed by Danish Raza ` |

**Output:**

No Yes

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