Puzzle 5: What does it mean by Hex and Octal literals are negative if their high-order bit is set?

In the book, "Java Puzzle", Puzzle 5: The Joy of Hex, there is a bold line Hex and Octal literals are negative if their high-order bit is set to explain the number 0xcafebabe is equivalent to the decimal value -889275714.

So what does "high-order bit is set" mean?

"high-order bit" is the left most bit of a given type. For example, if type is integer, which has 32 bits, then the high-order bit is the 32nd bit counting from right to left.

The 32nd bit counting from right to left is 0 in the following case, so the number is a positive number

int max = Integer.valueOf("01111111111111111111111111111111", 2);
System.out.println(max);

The result is

2147483647

which happens to be the maximum integer number.

Now let's convert the Hex format number 0xcafebabe to binary format

String s = Integer.toBinaryString(0xcafebabe);

The result is

11001010111111101011101010111110

The high-order bit is 1, therefore, it is a negative number.