Java and python ^ operator

Question

For a CompSci class, we were reviewing the Java Math class. Being the foolish programmer that I am, I tried using the ^ operator instead of the Math.pow function. Surprise, Surprise, it did not work. But, what Java spit out, is my question. I am trying to figure out the operation that is being done with the numbers. You can see what I am talking about below.

System.out.println(5^1);
System.out.println(5^2);
System.out.println(5^3);
System.out.println(5^4);
System.out.println(5^5);
System.out.println(5^6);
System.out.println(5^7);
System.out.println(5^8);
System.out.println(5^9);

Running the above, I get the following:

The same thing happens when I do the equivalent in Python (print 5^1, etc...). The Java API doc says that the ^ is a "bitwise exclusive OR", but that still does not help with how have gets 6 from 5 and 3. Could someone explain why this is happening?

Did you consider looking in the Java Language Specification? — user207421
– user207421, Commented Oct 26, 2012 at 2:22
Why the hell was this question closed? Are 10 answers not enough to prove that it is actually pretty easy to tell "what is being asked here"? — Yuval Adam
– Yuval Adam, Commented Oct 30, 2012 at 18:39
Why did you choose to ask here instead of simply googling bitwise exclusive OR? — Overv
– Overv, Commented Nov 1, 2012 at 13:39

Yuval Adam · Accepted Answer · 2012-10-25 17:27:45Z

15

This is a bitwise operation, and thus it operates on the binary bits of your numbers. 6 is 110 in binary form. 5 is 101 in binary form.

110
101
=== (^ xor)
011

011 is 3 in binary.

Read up on https://en.wikipedia.org/wiki/Exclusive_or

answered Oct 25, 2012 at 17:27

Yuval Adam

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Comments

Florin Stingaciu · Accepted Answer · 2012-10-25 17:30:57Z

3

Okay so lets take the first example. The easiest one. Take 5^1.

5 can be represented in binary like so 101 and one can be represented like so 001.

101    XOR
001
---
100 = 4 (in decimal)

Because 1 XOR 1 = 0, 0 XOR 0 = 0 and 1 XOR 0 = 1. Just go and check out the wiki page on XOR.

answered Oct 25, 2012 at 17:30

Florin Stingaciu

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Comments

Alex · Accepted Answer · 2012-10-25 17:28:46Z

2

This is the XOR operation.

5 = 101 in binary
3 = 011 in binary

    101
XOR 011 
  = 110 = 6 in decimal

answered Oct 25, 2012 at 17:28

Alex

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Comments

Rohit Jain · Accepted Answer · 2012-10-25 17:28:49Z

1

^ is BitWise XOR operator. So,

5 ^ 1: -

101 -> 5
001 -> 1
--- XOR
100 = 4

1 XOR 1 = 0
1 XOR 0 = 1

See these links: -

answered Oct 25, 2012 at 17:28

Rohit Jain

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Comments

Community · Accepted Answer · 2017-05-23 12:21:18Z

1

^ is the bitwise XOR operation, and it's truth table looks like this:

  | 0 | 1 |
0 | 0 | 1 |
1 | 1 | 0 |

So the output bit is 1 only when the inputs are different, and 0 otherwise. So 5 ^ 3 looks like this:

  0000 0101 (5)
^ 0000 0011 (3)
= 0000 0110 (6)

So it's doing exactly what it's supposed to. Take a look at the Nuts and Bolts tutorial for bitwise operations and this SO question for more references.

edited May 23, 2017 at 12:21

CommunityBot

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answered Oct 25, 2012 at 17:29

Brian

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1 Comment

user207421 Over a year ago

Best answer by far, because of the truth table. +1

Dmitriy Sukharev · Accepted Answer · 2012-10-25 17:29:44Z

1

It's because of binary representation of five is 101b, of three is 011b.

Xor works in the following way:

0 xor 0 = 0
0 xor 1 = 1
1 xor 0 = 1
1 xor 1 = 0

Therefore: 101 xor 011 = 110 that is binary representation of six.

answered Oct 25, 2012 at 17:29

Dmitriy Sukharev

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Comments

Ted Hopp · Accepted Answer · 2012-10-25 17:33:43Z

1

In Java, the ^ operator when applied to int arguments is bitwise exclusive-or. That explains the output. For the particular case of 5 and 3:

101 (5)
011 (3)
---
110 (6)

Note that for logical arguments, it is logical exclusive-or. In that case (b1 ^ b2) == (b1 != b2).

edited Oct 25, 2012 at 17:33

answered Oct 25, 2012 at 17:28

Ted Hopp

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Comments

Noctis Skytower · Accepted Answer · 2012-10-25 18:52:01Z

Hope this little program helps to explain the exclusive-or operator better using the examples it prints:

>>> for x, y in ((x, y) for x in range(11) for y in range(x, 11)):
    print('''{0} ^ {1} = {2} (Why?)
Because:
{0:04b} = {0}
^^^^
{1:04b} = {1}
====
{2:04b} = {2}
'''.format(x, y, x ^ y))


0 ^ 0 = 0 (Why?)
Because:
0000 = 0
^^^^
0000 = 0
====
0000 = 0

0 ^ 1 = 1 (Why?)
Because:
0000 = 0
^^^^
0001 = 1
====
0001 = 1

0 ^ 2 = 2 (Why?)
Because:
0000 = 0
^^^^
0010 = 2
====
0010 = 2

0 ^ 3 = 3 (Why?)
Because:
0000 = 0
^^^^
0011 = 3
====
0011 = 3

0 ^ 4 = 4 (Why?)
Because:
0000 = 0
^^^^
0100 = 4
====
0100 = 4

0 ^ 5 = 5 (Why?)
Because:
0000 = 0
^^^^
0101 = 5
====
0101 = 5

0 ^ 6 = 6 (Why?)
Because:
0000 = 0
^^^^
0110 = 6
====
0110 = 6

0 ^ 7 = 7 (Why?)
Because:
0000 = 0
^^^^
0111 = 7
====
0111 = 7

0 ^ 8 = 8 (Why?)
Because:
0000 = 0
^^^^
1000 = 8
====
1000 = 8

0 ^ 9 = 9 (Why?)
Because:
0000 = 0
^^^^
1001 = 9
====
1001 = 9

0 ^ 10 = 10 (Why?)
Because:
0000 = 0
^^^^
1010 = 10
====
1010 = 10

1 ^ 1 = 0 (Why?)
Because:
0001 = 1
^^^^
0001 = 1
====
0000 = 0

1 ^ 2 = 3 (Why?)
Because:
0001 = 1
^^^^
0010 = 2
====
0011 = 3

1 ^ 3 = 2 (Why?)
Because:
0001 = 1
^^^^
0011 = 3
====
0010 = 2

1 ^ 4 = 5 (Why?)
Because:
0001 = 1
^^^^
0100 = 4
====
0101 = 5

1 ^ 5 = 4 (Why?)
Because:
0001 = 1
^^^^
0101 = 5
====
0100 = 4

1 ^ 6 = 7 (Why?)
Because:
0001 = 1
^^^^
0110 = 6
====
0111 = 7

1 ^ 7 = 6 (Why?)
Because:
0001 = 1
^^^^
0111 = 7
====
0110 = 6

1 ^ 8 = 9 (Why?)
Because:
0001 = 1
^^^^
1000 = 8
====
1001 = 9

1 ^ 9 = 8 (Why?)
Because:
0001 = 1
^^^^
1001 = 9
====
1000 = 8

1 ^ 10 = 11 (Why?)
Because:
0001 = 1
^^^^
1010 = 10
====
1011 = 11

2 ^ 2 = 0 (Why?)
Because:
0010 = 2
^^^^
0010 = 2
====
0000 = 0

2 ^ 3 = 1 (Why?)
Because:
0010 = 2
^^^^
0011 = 3
====
0001 = 1

2 ^ 4 = 6 (Why?)
Because:
0010 = 2
^^^^
0100 = 4
====
0110 = 6

2 ^ 5 = 7 (Why?)
Because:
0010 = 2
^^^^
0101 = 5
====
0111 = 7

2 ^ 6 = 4 (Why?)
Because:
0010 = 2
^^^^
0110 = 6
====
0100 = 4

2 ^ 7 = 5 (Why?)
Because:
0010 = 2
^^^^
0111 = 7
====
0101 = 5

2 ^ 8 = 10 (Why?)
Because:
0010 = 2
^^^^
1000 = 8
====
1010 = 10

2 ^ 9 = 11 (Why?)
Because:
0010 = 2
^^^^
1001 = 9
====
1011 = 11

2 ^ 10 = 8 (Why?)
Because:
0010 = 2
^^^^
1010 = 10
====
1000 = 8

3 ^ 3 = 0 (Why?)
Because:
0011 = 3
^^^^
0011 = 3
====
0000 = 0

3 ^ 4 = 7 (Why?)
Because:
0011 = 3
^^^^
0100 = 4
====
0111 = 7

3 ^ 5 = 6 (Why?)
Because:
0011 = 3
^^^^
0101 = 5
====
0110 = 6

3 ^ 6 = 5 (Why?)
Because:
0011 = 3
^^^^
0110 = 6
====
0101 = 5

3 ^ 7 = 4 (Why?)
Because:
0011 = 3
^^^^
0111 = 7
====
0100 = 4

3 ^ 8 = 11 (Why?)
Because:
0011 = 3
^^^^
1000 = 8
====
1011 = 11

3 ^ 9 = 10 (Why?)
Because:
0011 = 3
^^^^
1001 = 9
====
1010 = 10

3 ^ 10 = 9 (Why?)
Because:
0011 = 3
^^^^
1010 = 10
====
1001 = 9

4 ^ 4 = 0 (Why?)
Because:
0100 = 4
^^^^
0100 = 4
====
0000 = 0

4 ^ 5 = 1 (Why?)
Because:
0100 = 4
^^^^
0101 = 5
====
0001 = 1

4 ^ 6 = 2 (Why?)
Because:
0100 = 4
^^^^
0110 = 6
====
0010 = 2

4 ^ 7 = 3 (Why?)
Because:
0100 = 4
^^^^
0111 = 7
====
0011 = 3

4 ^ 8 = 12 (Why?)
Because:
0100 = 4
^^^^
1000 = 8
====
1100 = 12

4 ^ 9 = 13 (Why?)
Because:
0100 = 4
^^^^
1001 = 9
====
1101 = 13

4 ^ 10 = 14 (Why?)
Because:
0100 = 4
^^^^
1010 = 10
====
1110 = 14

5 ^ 5 = 0 (Why?)
Because:
0101 = 5
^^^^
0101 = 5
====
0000 = 0

5 ^ 6 = 3 (Why?)
Because:
0101 = 5
^^^^
0110 = 6
====
0011 = 3

5 ^ 7 = 2 (Why?)
Because:
0101 = 5
^^^^
0111 = 7
====
0010 = 2

5 ^ 8 = 13 (Why?)
Because:
0101 = 5
^^^^
1000 = 8
====
1101 = 13

5 ^ 9 = 12 (Why?)
Because:
0101 = 5
^^^^
1001 = 9
====
1100 = 12

5 ^ 10 = 15 (Why?)
Because:
0101 = 5
^^^^
1010 = 10
====
1111 = 15

6 ^ 6 = 0 (Why?)
Because:
0110 = 6
^^^^
0110 = 6
====
0000 = 0

6 ^ 7 = 1 (Why?)
Because:
0110 = 6
^^^^
0111 = 7
====
0001 = 1

6 ^ 8 = 14 (Why?)
Because:
0110 = 6
^^^^
1000 = 8
====
1110 = 14

6 ^ 9 = 15 (Why?)
Because:
0110 = 6
^^^^
1001 = 9
====
1111 = 15

6 ^ 10 = 12 (Why?)
Because:
0110 = 6
^^^^
1010 = 10
====
1100 = 12

7 ^ 7 = 0 (Why?)
Because:
0111 = 7
^^^^
0111 = 7
====
0000 = 0

7 ^ 8 = 15 (Why?)
Because:
0111 = 7
^^^^
1000 = 8
====
1111 = 15

7 ^ 9 = 14 (Why?)
Because:
0111 = 7
^^^^
1001 = 9
====
1110 = 14

7 ^ 10 = 13 (Why?)
Because:
0111 = 7
^^^^
1010 = 10
====
1101 = 13

8 ^ 8 = 0 (Why?)
Because:
1000 = 8
^^^^
1000 = 8
====
0000 = 0

8 ^ 9 = 1 (Why?)
Because:
1000 = 8
^^^^
1001 = 9
====
0001 = 1

8 ^ 10 = 2 (Why?)
Because:
1000 = 8
^^^^
1010 = 10
====
0010 = 2

9 ^ 9 = 0 (Why?)
Because:
1001 = 9
^^^^
1001 = 9
====
0000 = 0

9 ^ 10 = 3 (Why?)
Because:
1001 = 9
^^^^
1010 = 10
====
0011 = 3

10 ^ 10 = 0 (Why?)
Because:
1010 = 10
^^^^
1010 = 10
====
0000 = 0

>>>

People are fairly good at recognizing patterns (ie, language). A rule should be rather easily derived from the examples.

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