Welcome to this quick but exciting lesson on Bit Manipulation Techniques. Bit manipulation is a powerful technique used in programming to efficiently solve problems that may seem complex or resource-intensive at first. By examining and manipulating the binary representations of data, we can create solutions that satisfy problem requirements while maintaining good time and space complexity.

In this lesson, we'll practice techniques such as setting and clearing bits, counting set bits, and bit masking. PHP's syntax allows for easy manipulation of binary data, making it a great choice for learning bit manipulation.

Take a look at the preview problem:

This method, countSetBits, counts the number of set bits (1s) in the binary representation of a number. The & operator is used for the bitwise AND operation. The $n - 1 operation flips the least significant bit (the rightmost 1 bit in the binary representation) of $n to 0, and $n &= ($n - 1) applies this change to $n. The while loop continues until $n becomes 0, and for each iteration, the count is increased, tracking the number of set bits.

For example, consider $n = 6, which is 110 in binary:

• $n - 1 is 5 (101 in binary);
• The bitwise AND operation 110 & 101 results in 100.
• After the first iteration, $n becomes 4 (100 in binary) and count is incremented to 1.
• $n - 1 is now 3 (011 in binary);
• The bitwise AND operation 100 & 011 results in 000.
• At this point, $n becomes 0 and the loop ends, with count being 2, which is the number of set bits in the original number 6.

The method then returns the count, which is 2, representing the two 1s in the binary representation of 6.

It's time to roll up your sleeves and put these techniques into practice. Our exercises will challenge you and help deepen your understanding of bit manipulation using PHP. Remember, the goal is not just to learn how to solve specific problems but to understand the fundamentals of bit manipulation and apply this knowledge to solve a wide variety of problems. Let's get started by practicing bit manipulation techniques in PHP!