Java Integer导致二进制混乱

Question

According to my comprehension, Integer type in Java is 32-bit-signed, the most significant bit is the signed bit. This is why Integer.MAX_VALUE is 2147483647 , which is:

1111111111111111111111111111111(1 repeated in 31 times).

So I assume that it actually can be represented as:

01111111111111111111111111111111(a 0 followed by 1 repeated 31 times)

The 0 means this is a positive integer.

Then for the following codes:

    int test = -2147483647;
    String converted = Integer.toBinaryString(test);
    System.out.println(converted);

The output is:

 10000000000000000000000000000001

Why the output is like above? For me, the binary stream should be represented as -1 , since the most significant bit is 1 means negative.

Like this:

    int minusOne = -1;
    String converted1 = Integer.toBinaryString(test);
    System.out.println(converted1);

The output is the same as above:

10000000000000000000000000000001

Any explanation?

Answer 1

Look at the folowing two snippets, did you find the problem:

int test = -2147483647;
String converted = Integer.toBinaryString(test);
System.out.println(converted);

int minusOne = -1;
String converted1 = Integer.toBinaryString(test);
System.out.println(converted1);

You are printing out the same variable test, that's why the output is the same. If you printout "minusOne" it would be all 1's.

10000000000000000000000000000001 -> -2147483647 = Integer.MIN_VALUE + 1
11111111111111111111111111111111 -> -1

1111111111111111111111111111111  -> Integer.MAX_VALUE = 2147483647
10000000000000000000000000000000 -> Integer.MAX_VALUE + 1
10000000000000000000000000000000 -> Integer.MIN_VALUE = -2147483648
10000000000000000000000000000001 -> Integer.MIN_VALUE + 1

Answer 2

In addition to @dragon66's point, be aware that these are two's complement numbers. They are not represented as sign, magnitude.

In two's complement representation, one negates a number by inverting all the bits, then adding 1. This way, there's only one representation of 0.