Have you ever come across the concept of why `~1` doesn't equal to `2` in the world of bitwise operations in programming? It might seem counterintuitive at first, but there's a clever explanation behind it. Let's delve into the fascinating world of bitwise operations and uncover the mystery behind this subtle quirk.
In the realm of bitwise operations, the `~` operator is used for bitwise negation, also known as the bitwise NOT operation. When you apply the `~` operator to a binary number, it performs a bitwise inversion on each bit of the number. It flips all the bits from 1 to 0 and from 0 to 1.
So why does `~1` not equal to `2`? To understand this, we need to consider how numbers are represented in binary form and how bitwise operations manipulate these binary representations.
In binary representation, the number 1 is represented as `0001`. Now, when you apply the bitwise NOT operation to the binary representation of 1 (`0001`), it flips each bit, resulting in `1110`. This binary representation corresponds to the signed 2's complement form of `-2` in decimal.
Therefore, when you evaluate `~1` in the context of bitwise operations, it equals `-2`, not `2`. This discrepancy arises due to the way negative numbers are represented in binary through the use of 2's complement notation.
In 2's complement representation, the most significant bit (leftmost bit) indicates the sign of the number, with `0` representing a positive number and `1` representing a negative number. The rest of the bits store the magnitude of the number.
When the bitwise NOT operation is applied to a positive number, the result is a negative number in 2's complement form. In our case, `~1` translates to `-2` in decimal.
So, the key takeaway here is that bitwise operations, especially the bitwise NOT operation, work at the level of individual bits and can produce unexpected results if you're not familiar with binary representations and 2's complement notation.
To summarize, the reason why `~1` does not equal `2` lies in the intricacies of binary representation and 2's complement notation. By understanding how bitwise operations manipulate binary numbers, you can make sense of seemingly perplexing outcomes like this one. Keep exploring the world of bitwise operations, and you'll unlock a whole new dimension of programming insights!
In conclusion, next time you encounter the puzzling scenario of `~1` not equaling `2`, remember the magic happening behind the scenes in the realm of bitwise operations. Happy coding!