Welcome to this focused lesson on Bit Manipulation Techniques. Bit manipulation is a powerful tool for solving problems efficiently by working directly with binary representations. It allows us to achieve both time and space efficiency by using bitwise operations to handle data at the binary level.

In this lesson, we’ll explore essential bit manipulation techniques like setting, clearing, and counting bits, as well as bit masking. We’ll implement these concepts in Ruby, showcasing the language’s ability to handle low-level operations in a clean, readable way.

Let's dive into an example that demonstrates a common bit manipulation technique — counting set bits (1s) in a number’s binary form.

In this function:

1. &= performs a bitwise AND operation with n and n - 1. This operation effectively flips the least significant 1 bit in n to 0.

2. For each iteration, count increments, tracking each 1 bit encountered. The loop continues until n becomes 0, clearing each bit in sequence.

For instance, with n = 6 (110 in binary):

• n - 1 becomes 5 (101 in binary).
• The bitwise AND operation 110 & 101 results in , flipping the rightmost bit to .

In Ruby, bitwise operations provide a direct way to interact with binary data. Here are some of the most frequently used operations:

• Bitwise AND (&): Sets each bit to 1 if both bits are 1.
• Bitwise OR (|): Sets each bit to 1 if at least one of the bits is 1.
• Bitwise XOR (^): Sets each bit to 1 only if the bits are different.
• Bitwise NOT (~): Inverts all the bits, switching 1s to 0s and vice versa.
• Left Shift (<<): Shifts all bits to the left, filling in 0s from the right.
• Right Shift (>>): Shifts all bits to the right, filling in 0s from the left.

These operations are foundational for efficiently performing tasks that would otherwise require more complex logic or would take longer when using higher-level constructs.

Now, 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 with Ruby.

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!