How is System.out.println(4*2147483647) equal to -4 in java?

Question

I am a Java beginner and pretty confused with this.

How is System.out.println(4*2147483647) equal to -4 in java?

Answer 1

It is due to integer silent overflow.

2147483647 == Integer.MAX_VALUE is the maximum value for an integer.

Silent overflow means that 2147483647 + 1 == Integer.MIN_VALUE = -2147483648
You can then see that 2147483647 + 2147483647 == 2147483647 + (-2147483648 + - 1) == -2

In other words, 2147483647 * 2 == -2, and you can now see why 2147483647 * 4 == -4.

More technically, the result is defined by the Java Language Specification #15.17.1:

If an integer multiplication overflows, then the result is the low-order bits of the mathematical product as represented in some sufficiently large two's-complement format. As a result, if overflow occurs, then the sign of the result may not be the same as the sign of the mathematical product of the two operand values.

Answer 2

It has to do with the way processors perform a binary mutiplication. The number you have in there is the maximum signed integer, which is represented as 0111111111111111111111111 (I haven't checked the number of ones there, but I assume you get the idea).

When you mutiply by 4, is like doing a left shift by 2, which results in 11111111111111111111100 (which represents -4). You might want to read how mutiplication is done in binary.

Answer 3

Because the result is out of the range of an int. Primitive Data Types

To solve this, use a long instead of an int.

Answer 4

The problem is that you are using int (4 bytes) and not long (8 bytes)

System.out.println(4*2147483647);

Try adding an l (for lema) after one of the numbers so that the result is a long and not an Integer. Integer has a max value smaller than your result http://docs.oracle.com/javase/1.4.2/docs/api/java/lang/Integer.html#MAX_VALUE

System.out.println(4l * 2147483647);

or

System.out.println(4 * 2147483647l);

The above two give the correct result. That is 8589934588

Answer 5

Most integers in computer system based on 32-bit which means 4 byte (you can use 64bit or much too). You can have maximum 4,294,967,295 in a 32bit integer. So 4,294,967,295 + 5 will cause overflow give you 5. Also -1 means 4,294,967,295 in integer. Because there is a negative bit.

More Info: http://en.wikipedia.org/wiki/Integer_overflow

http://en.wikipedia.org/wiki/Integer_(computer_science)

Answer 6

It's because of how a computer stores numbers in memory. 2147483647 * 4 = 8589934588

8589934588 in binary results in 1 1111 1111 1111 1111 1111 1111 1111 1100

The first one is a bit which signifies the number it preceeds is negative.

The next part can be explained with two's complement.

Two's complement is a way to represent negative values which in calculated by invering all bits, then adding one. This will result in 0011 (the inversion of the last 4 bytes) then adding one causes it to be 0100 which is the binary representation of 4.

Because the sign bit is on negative, it results in -4