What does the ^ operator do in Java?

The ^ operator in Java

^ in Java is the exclusive-or ("xor") operator.

Let's take 5^6 as example:

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

This the truth table for bitwise (JLS 15.22.1) and logical (JLS 15.22.2) xor:

^ | 0 1      ^ | F T
--+-----     --+-----
0 | 0 1      F | F T
1 | 1 0      T | T F

More simply, you can also think of xor as "this or that, but not both!".

Exponentiation in Java

As for integer exponentiation, unfortunately Java does not have such an operator. You can use double Math.pow(double, double) (casting the result to int if necessary).

You can also use the traditional bit-shifting trick to compute some powers of two. That is, (1L << k) is two to the k-th power for k=0..63.

Horner's scheme

Addressing your specific need, you actually don't need to compute various powers of 10. You can use what is called the Horner's scheme, which is not only simple but also efficient.

Since you're doing this as a personal exercise, I won't give the Java code, but here's the main idea:

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

It may look complicated at first, but it really isn't. You basically read the digits left to right, and you multiply your result so far by 10 before adding the next digit.

In table form:

step   result  digit  result*10+digit
   1   init=0      8                8
   2        8      6               86
   3       86      7              867
   4      867      5             8675
   5     8675      3            86753
   6    86753      0           867530
   7   867530      9          8675309=final

As many people have already pointed out, it's the XOR operator. Many people have also already pointed out that if you want exponentiation then you need to use Math.pow.

But I think it's also useful to note that ^ is just one of a family of operators that are collectively known as bitwise operators:

Operator    Name         Example     Result  Description
a & b       and          3 & 5       1       1 if both bits are 1.
a | b       or           3 | 5       7       1 if either bit is 1.
a ^ b       xor          3 ^ 5       6       1 if both bits are different.
~a          not          ~3          -4      Inverts the bits.
n << p      left shift   3 << 2      12      Shifts the bits of n left p positions. Zero bits are shifted into the low-order positions.
n >> p      right shift  5 >> 2      1       Shifts the bits of n right p positions. If n is a 2's complement signed number, the sign bit is shifted into the high-order positions.
n >>> p     right shift  -4 >>> 28   15      Shifts the bits of n right p positions. Zeros are shifted into the high-order positions.

From here.

These operators can come in handy when you need to read and write to integers where the individual bits should be interpreted as flags, or when a specific range of bits in an integer have a special meaning and you want to extract only those. You can do a lot of every day programming without ever needing to use these operators, but if you ever have to work with data at the bit level, a good knowledge of these operators is invaluable.

It's bitwise XOR, Java does not have an exponentiation operator, you would have to use Math.pow() instead.

XOR operator rule =>

0 ^ 0 = 0
1 ^ 1 = 0
0 ^ 1 = 1
1 ^ 0 = 1

Binary representation of 4, 5 and 6 :

4 = 1 0 0 
5 = 1 0 1
6 = 1 1 0

now, perform XOR operation on 5 and 4:

     5 ^ 4 => 1  0  1   (5)
              1  0  0   (4)
            ----------
              0  0  1   => 1

Similarly,

5 ^ 5 => 1   0   1    (5)
         1   0   1    (5)
       ------------
         0   0   0   => (0)


5 ^ 6 => 1   0   1  (5)
         1   1   0  (6)
        -----------
         0   1   1  => 3

It is the XOR bitwise operator.

What does the ^ operator do in Java?

The ^ operator in Java

See also

Exponentiation in Java

See also

Horner's scheme

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