What Does the `^` Operator Do in Java, and How Does it Differ from Exponentiation?

What Does the ^ Operator Do in Java?

In Java, the ^ operator serves as the exclusive-or ("xor") operator. Unlike exponentiation, it operates bitwise on integer values.

Bitwise XOR

The xor operator compares corresponding bits of two binary numbers. For each bit:

• If both bits are 0 or both are 1, the result is 0.
• If one bit is 0 and the other is 1, the result is 1.

Example

Consider the XOR operation of 5 (101 in binary) and 6 (110 in binary):

(decimal)   (binary)
     5     =  101
     6     =  110
------------------ xor
     3     =  011

The resulting bit pattern, 011, represents the decimal value 3.

Exponentiation in Java

Java lacks an integer exponentiation operator. To perform exponentiation, you can use Math.pow(double, double) (casting to int if necessary).

Alternatively, you can利用bit-shift trick to efficiently compute powers of two: (1L << k) equals two to the power of k for k in the range 0 to 63.

Horner's Scheme

In the specific case of converting a string of digits to an integer, you can use Horner's scheme. This method is both simple and efficient:

8675309 = 8*10^6 + 6*10^5 + 7*10^4 + 5*10^3 + 3*10^2 + 0*10^1 + 9*10^0
        = (((((8*10 + 6)*10 + 7)*10 + 5)*10 + 3)*10 + 0)*10 + 9

Start with an initial result of 0. Read the digits from left to right and accumulate the result by multiplying by 10 and adding the current digit at each step.

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