Why 2*Integer.MAX_VALUE = -2?

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How does Java handle integer underflows and overflows and how would you check for it?
How is System.out.println(4*2147483647) equal to -4 in java?

I want to know why this holds:

2 * Integer.MAX_VALUE == -2

I'm look forward to your response.

[Integer overflow](http://en.wikipedia.org/wiki/Integer_overflow). — BalusC, Oct 23 '12 at 17:42
See here: http://stackoverflow.com/questions/3001836/how-does-java-handle-integer-underflows-and-overflows-and-how-would-you-check-fo — Jon B, Oct 23 '12 at 17:43
Lots of downvotes. Is this a particularly bad question? Fixed integer arithmetic is odd (and should be obscure). — Tom Hawtin - tackline, Oct 23 '12 at 17:46
I haven't down voted but I would assume its because its a quite often asked question (several answers on stack overflow) and the question probably lacks any research. — Scorpion, Oct 23 '12 at 17:50
@Scorpion Best to close as duplicate rather than downvoting. I haven't seen it (only looking at the Java tag, which may explain it). — Tom Hawtin - tackline, Oct 23 '12 at 17:57
@TomHawtin-tackline I agree and that's why no down votes from me. — Scorpion, Oct 24 '12 at 04:27

score 6 · Answer 1 · answered Oct 23 '12 at 17:42

6

You get this result because of an integer overflow: in a two's complement system of representing negative integers, taking the max value which is 011.....11₂ and multiplying it by 2 gives you 11.....110₂, which corresponds to -2.

answered Oct 23 '12 at 17:42

Sergey Kalinichenko

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score 1 · Answer 2 · answered Oct 23 '12 at 17:44

1

That is because of the Integer overflow.

answered Oct 23 '12 at 17:44

Rahul Tripathi

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score 1 · Answer 3 · answered Oct 23 '12 at 17:45

1

Integer.MAX_VALUE is 0x7FFFFFFF. Multiply by two and you get 0xFFFFFFFE (equivalent to shifting left one bit). This is a negative number (the first bit is 1) and is the binary representation of -2.

answered Oct 23 '12 at 17:45

Jim Garrison

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score 1 · Answer 4 · answered Oct 23 '12 at 17:45

This is because of two's complement, where the lef most bit is used to signify if a number is positive (0) or negative (1). So when you add max int by itself (equivalent of multiplfy by two), this happens:

  011111111111111111111111
+ 011111111111111111111111
__________________________
  111111111111111111111110

and 111111111111111111111110 represents -2.

score 0 · Answer 5 · answered Oct 23 '12 at 18:11

The MAX_VALUE of Int is 2^31 - 1 = 2147483647 = 0111 1111 1111 1111 1111 1111 1111 1111(binary number) the highest bit (here is the first bit 0, indicates the integer is a positive number, when 1 indicates negative.

(suppose the length of an integer is 4bytes), 2 * MAX_VALUE,in computer an integer by 2 times is left shift(operator << ) on bits, eg. 2 << 1 = 4; 2 << 2 = 8; so 0111 1111 1111 1111 1111 1111 1111 1111 << 1 become 1111 1111 1111 1111 1111 1111 1111 1110 which is equal to -2 in decimal.

Why 2*Integer.MAX_VALUE = -2?

5 Answers5