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The ^= operator is the bitwise exclusive OR (XOR) compound assignment operator in Java. It evaluates the bitwise XOR between the left-hand operand and the right-hand operand, and subsequently assigns the computed result back to the left-hand operand.

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Syntax and Equivalence

leftOperand ^= rightOperand;
Internally, the Java compiler evaluates this expression as: 
leftOperand = (Type) (leftOperand ^ rightOperand);
The inclusion of the implicit cast (Type) is a critical language feature. If the left operand is of a type narrower than int (such as byte, short, or char), the bitwise operation is performed using 32-bit int promotion. The compound assignment operator automatically handles the narrowing primitive conversion back to the original type, preventing potential compilation errors.

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Mechanics on Integral Types

When applied to integer types (byte, short, int, long, char), the operator compares the binary representations of both operands bit by bit. The resulting bit is 1 if the corresponding bits in the operands are different, and 0 if they are identical. Truth Table for Bitwise XOR:
  • 0 ^ 0 = 0
  • 0 ^ 1 = 1
  • 1 ^ 0 = 1
  • 1 ^ 1 = 0
Execution Example: 
int a = 10; // Binary representation: 1010
int b = 6;  // Binary representation: 0110

a ^= b;     // Bitwise XOR evaluation:
            //   1010
            // ^ 0110
            // ---
            //   1100 (Decimal 12)

// 'a' is now assigned the value 12

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Mechanics on Boolean Types

When applied to boolean operands, ^= functions as a logical XOR assignment. It evaluates to true if and only if the left and right operands possess strictly opposing boolean values. Execution Example: 
boolean state = true;

state ^= false; // true ^ false -> true. 'state' remains true.
state ^= true;  // true ^ true  -> false. 'state' becomes false.
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