PHP Programming

PHP Bitwise Operations

A bitwise operation is an operation that works on the individual bits of a number.  Yes, that means the binary(base 2) representation of a number.  These bitwise operations work by exploiting properties of binary numbers to their advantage.  For instance, if the binary representation of a number ends with a 1, it’s odd.

Base 2 Refresher

For those of us who don’t manipulate bits every day (including myself), I thought that a quick refresher on binary representation would be a good idea.  First, let’s create a table.

4 3 2 1 0
0 0 0 0 1

Each column in the table represents a power of 2.  The first column (from the right) represents 20, the second 21, and so on.  Notice that I have a 1 in the row below the 0 column.  That stands for 20, and 20 is equal to 1.  Therefore, the number represented above (00001) is equal to 1.  On to the next table.

4 3 2 1 0
0 0 1 1 1
Now the base-2 number in the bottom row is 00111.  This is equal to 22 + 21 + 20, or 4 + 2 + 1, which is equal to 7.  As you can see, using binary representation is pretty easy.  On to our final example.
4 3 2 1 0
1 1 0 0 1
This example a bit (har, har) trickier.  The base-2 number in the bottom row is 11001, which is  24 + 23 +20(16 + 8 + 1) = 25.  Notice if there are zeros in the columns, we just ignore them completely.
And that’s it!  Base-2 representation of numbers is easy, and critical for every programmer to understand.  Now on to some tricks.

Trick 1 : Odd / Even

One of the most useful bitwise tricks for web developers is for determining if a number is even or odd.

for($i = 0; $i < 10; $i++) {
     if($i & 1) {
          echo "This is odd.";
     } else {
          echo "This is even.";
So how does help your web development?  Alternating rows.  If you deal with data in a tabular format, you nearly always need to alternate row color on a table.  Using the bitwise “AND” operator is a good way to accomplish this.

Trick 2 : Multiplication and Division

Using the left-shift (<<) and right-shift (>>) operators, we can easily divide and multiple by powers of two.  These operators aren’t limited to powers of two, but it makes things easier to understand.
//Example 1
$x = 2;
echo $x &lt;&lt; 1; //4
echo $x &lt;&lt; 2; //8
//Example 2
$x = 16;
echo $x &gt;&gt; 1; //8
echo $x &gt;&gt; 2; //4

In example 1, we left shift the number 2 one place.  By left shifting 1 place, it’s the same as multiplying that number by 2.  By left shifting 2 places, it’s the same multiplying the number by 2 twice.

Example 2 is doing bitwise division.  Right shifting by 1 place is the same as dividing the number by 2.  Right shifting by 2 places, is the same is the same as dividing the number by 2 twice.


There are most definitely a ton of other uses for bitwise operators, however these are the ones I use the most.  If you happen to have a favorite, please let everyone know about it in the comments.

For a more in depth introduction to bitwise operations please check out and

By Jack Slingerland

Founder of Working and living in Raleigh, NC. I manage a team of software engineers and work in Python, Django, TypeScript, Node.js, React+Redux, Angular, and PHP. I enjoy hanging out with my wife and son, lifting weights, and advancing in my free time.

9 replies on “PHP Bitwise Operations”

Could you give some other examples please? What would be the benefit of using Trick 1 with & 1 instead % 2? Why would I would << 2 in Trick 2 when I could use *4 and so on. I've been doing PHP for 10 years now and the only time I really used bitwise operators if for bitmasks, which no one uses nowadays anymore.

Jack, thank you. I have to admit, I had hoped for something more practical though. While bitwise operations are indeed somewhat faster, the difference is totally and utterly neglectable unless you are doing millions of computations. This is even less measurable than the infamous single quotes versus double quotes “optimization”.

I’d say the majority of programmers of PHP are not familiar with bitwise operations, so my suggestion would be not to confuse people with the bitwise solution just to shed some nanoseconds.

That’s not to say the article is bad. It’s good. I think it’s mentally stimulating and enjoyable. It’s just not that practical.

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