C++ Exercise 1 Continuation: Mastering Bitwise XOR Operations

Bitwise XOR (exclusive OR) is a binary operation that works on the individual bits of binary numbers. Here’s a detailed explanation:

Bitwise XOR Operation

• Symbol: The XOR operation is represented by the caret symbol (^) in C++.
• Operation: For each bit in the binary representation of two numbers, XOR returns 1 if the bits are different and 0 if they are the same.

Truth Table for XOR

Note: When both bits are same returns '0' ex: 0 ^0 = 0 or 1^1 = 0 else '1' ex: 1^0 = 1

Example of Bitwise XOR (a ^ b)

Let's consider two numbers:

• a = 5 (binary: 0101)
• b = 10 (binary: 1010)

Performing the XOR operation bitwise:

1. Write the Binary Representations

Perform XOR Operation

XOR compares each bit of a with the corresponding bit of b:

• Bit 1: 0 ^ 1 results in 1 (because the bits are different).
• Bit 2: 1 ^ 0 results in 1 (because the bits are different).
• Bit 3: 0 ^ 1 results in 1 (because the bits are different).
• Bit 4: 1 ^ 0 results in 1 (because the bits are different).

Combining these results:

a^b --> 1111

1. So, a ^ b results in 15 in decimal.

Using XOR for Swapping Variables

The XOR swap method allows you to swap the values of two variables without using a temporary variable. Here's how it works:

XOR Swap Steps

1. Step 1: a = a ^ b
2. Step 2: b = a ^ b
3. Step 3: a = a ^ b

Behind Scence

• Initially: a = 5 and b = 10
• After a = a ^ b ==> a = 15 and b = 10
• After b = a ^ b ==> a = 15 and b = 5
• After a = a ^ b ==> a = 10 and b = 5

In the end, the values of a and b have been swapped:

• Original a (5) is now b (5).
• Original b (10) is now a (10).

Conclusion

Bitwise XOR is a powerful operation used in various algorithms and problems. It can be particularly useful for efficiently swapping values and is a good example of how bitwise operations can be applied in practical programming scenarios.

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