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.

## Best Solution

Here is the Windows API you can call into. It's in wininet.dll and called InternetGetConnectedState.