Hello Guys, How are you all? Hope You all Are Fine. Today We Are Going To learn about **How to check if a given number is a power of two** **in Python**. So Here I am Explain to you all the possible Methods here.

Without wasting your time, Let’s start This Article.

Table of Contents

## How to check if a given number is a power of two?

**How to check if a given number is a power of two?**The binary representation of 4 is 100 and the binary representation of 3 is 011 (remember the & takes the binary representation of these numbers).

**check if a given number is a power of two**The binary representation of 4 is 100 and the binary representation of 3 is 011 (remember the & takes the binary representation of these numbers).

## Method 1

There’s a simple trick for this problem:

bool IsPowerOfTwo(ulong x) { return (x & (x - 1)) == 0; }

Note, this function will report `true`

for `0`

, which is not a power of `2`

. If you want to exclude that, here’s how:

bool IsPowerOfTwo(ulong x) { return (x != 0) && ((x & (x - 1)) == 0); }

### Explanation

First and foremost the bitwise binary & operator from MSDN definition:

Binary & operators are predefined for the integral types and bool. For integral types, & computes the logical bitwise AND of its operands. For bool operands, & computes the logical AND of its operands; that is, the result is true if and only if both its operands are true.

Now let’s take a look at how this all plays out:

The function returns boolean (true / false) and accepts one incoming parameter of type unsigned long (x, in this case). Let us for the sake of simplicity assume that someone has passed the value 4 and called the function like so:

bool b = IsPowerOfTwo(4)

Now we replace each occurrence of x with 4:

return (4 != 0) && ((4 & (4-1)) == 0);

Well we already know that 4 != 0 evals to true, so far so good. But what about:

((4 & (4-1)) == 0)

This translates to this of course:

((4 & 3) == 0)

But what exactly is `4&3`

?

The binary representation of 4 is 100 and the binary representation of 3 is 011 (remember the & takes the binary representation of these numbers). So we have:

100 = 4 011 = 3

Imagine these values being stacked up much like elementary addition. The `&`

operator says that if both values are equal to 1 then the result is 1, otherwise it is 0. So `1 & 1 = 1`

, `1 & 0 = 0`

, `0 & 0 = 0`

, and `0 & 1 = 0`

. So we do the math:

100 011 ---- 000

The result is simply 0. So we go back and look at what our return statement now translates to:

return (4 != 0) && ((4 & 3) == 0);

Which translates now to:

return true && (0 == 0);

return true && true;

We all know that `true && true`

is simply `true`

, and this shows that for our example, 4 is a power of 2.

## Method 2

`return (i & -i) == i`

**Summery**

It’s all About this issue. Hope all Methods helped you a lot. Comment below Your thoughts and your queries. Also, Comment below which Method worked for you? Thank You.

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