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