Why does the negative of Integer.MIN_VALUE give th

Question

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Math.abs returns wrong value for Integer.Min_VALUE (7 answers)

Closed 4 years ago.

Consider the below java code.

Integer value = Integer.MIN_VALUE;
System.out.println(value);

value = -value;
System.out.println(value);

Output

-2147483648
-2147483648

How the negative value of Integer.MIN_VALUE value results the same value?

However the result can't be 2147483648 because the maximum value of Integer in java is 2147483647.

But want to know why -2147483648? What kind of bit-wise operations are happening internally?

Answer 1

When you negate -2147483648, it resolves to 2147483648, which exceeds the Integer.MAX_VALUE with 1. Then the value overflows to Integer.MIN_VALUE again.

From the JLS:

The integral types are byte, short, int, and long, whose values are 8-bit, 16-bit, 32-bit and 64-bit signed two's-complement integers.

So, every unary operation done on an integer will actually be applied on the two's complement representation of the number. When the Integer.MAX_VALUE is reached it will consist of a leading 0 and 31 1 bits. Adding 1 would make it a number with a leading 1 and 31 trailing 0s, which is actually the two's complement representation of Integer.MIN_VALUE.

Answer 2

What kind of bit-wise operations are happening internally?

Java uses two's complement representation of signed numbers. Therefore, the change of sign operation, consists of two steps:

1. Inverting the bits of the original value, and
2. Adding 1 to the result.

2147483648's representation is shown below:

10000000000000000000000000000000

Inverting it produces

01111111111111111111111111111111

Adding 1 makes it the same number again, i.e.

10000000000000000000000000000000

due to integer overflow.