Understanding the Caret (^) Operator in Python

The caret operator (^) in Python performs a bitwise exclusive OR (XOR) operation between its two operands. In other words, it evaluates to True if its arguments differ (one is True, the other is False) and evaluates to False if they are the same.

To demonstrate, consider the following examples:

>>> 0 ^ 0
0
>>> 1 ^ 1
0
>>> 1 ^ 0
1
>>> 0 ^ 1
1

Now, let's understand one of the examples you encountered:

>>> 8 ^ 3
11

This can be broken down into the following binary representation:

1000  # 8 (binary)
0011  # 3 (binary)
----  # APPLY XOR ('vertically')
1011  # result = 11 (binary)

As you can see, the XOR operation is performed bit-by-bit, resulting in a binary value of 1011, which is equivalent to 11 in decimal.