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

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.

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

1. 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).

2. 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.