In C, the language itself does not determine the representation of certain datatypes. It can vary from machine to machine, on embedded systems the int can be 16 bit wide, though usually it is 32 bit.

The only requirement is that short int <= int <= long int by size. Also, there is a recommendation that int should represent the native capacity of the processor.

All types are signed. The unsigned modifier allows you to use the highest bit as part of the value (otherwise it is reserved for the sign bit).

Here's a short table of the possible values for the possible data types:

          width                     minimum                         maximum
signed    8 bit                        -128                            +127
signed   16 bit                     -32 768                         +32 767
signed   32 bit              -2 147 483 648                  +2 147 483 647
signed   64 bit  -9 223 372 036 854 775 808      +9 223 372 036 854 775 807
unsigned  8 bit                           0                            +255
unsigned 16 bit                           0                         +65 535
unsigned 32 bit                           0                  +4 294 967 295
unsigned 64 bit                           0     +18 446 744 073 709 551 615

In Java, the Java Language Specification determines the representation of the data types.

The order is: byte 8 bits, short 16 bits, int 32 bits, long 64 bits. All of these types are signed, there are no unsigned versions. However, bit manipulations treat the numbers as they were unsigned (that is, handling all bits correctly).

The character data type char is 16 bits wide, unsigned, and holds characters using UTF-16 encoding (however, it is possible to assign a char an arbitrary unsigned 16 bit integer that represents an invalid character codepoint)

          width                     minimum                         maximum

SIGNED
byte:     8 bit                        -128                            +127
short:   16 bit                     -32 768                         +32 767
int:     32 bit              -2 147 483 648                  +2 147 483 647
long:    64 bit  -9 223 372 036 854 775 808      +9 223 372 036 854 775 807

UNSIGNED
char     16 bit                           0                         +65 535

but as for this method, I don't understand the purpose of Integer.MAX_VALUE and Integer.MIN_VALUE.

By starting out with smallest set to Integer.MAX_VALUE and largest set to Integer.MIN_VALUE, they don't have to worry later about the special case where smallest and largest don't have a value yet. If the data I'm looking through has a 10 as the first value, then numbers[i]<smallest will be true (because 10 is < Integer.MAX_VALUE) and we'll update smallest to be 10. Similarly, numbers[i]>largest will be true because 10 is > Integer.MIN_VALUE and we'll update largest. And so on.

Of course, when doing this, you must ensure that you have at least one value in the data you're looking at. Otherwise, you end up with apocryphal numbers in smallest and largest.

Note the point Onome Sotu makes in the comments:

...if the first item in the array is larger than the rest, then the largest item will always be Integer.MIN_VALUE because of the else-if statement.

Which is true; here's a simpler example demonstrating the problem (live copy):

public class Example
{
    public static void main(String[] args) throws Exception {
        int[] values = {5, 1, 2};
        int smallest = Integer.MAX_VALUE;
        int largest  = Integer.MIN_VALUE;
        for (int value : values) {
            if (value < smallest) {
                smallest = value;
            } else if (value > largest) {
                largest = value;
            }
        }
        System.out.println(smallest + ", " + largest); // 1, 2 -- WRONG
    }
}

To fix it, either:

1. Don't use else, or

2. Start with smallest and largest equal to the first element, and then loop the remaining elements, keeping the else if.

Here's an example of that second one (live copy):

public class Example
{
    public static void main(String[] args) throws Exception {
        int[] values = {5, 1, 2};
        int smallest = values[0];
        int largest  = values[0];
        for (int n = 1; n < values.length; ++n) {
            int value = values[n];
            if (value < smallest) {
                smallest = value;
            } else if (value > largest) {
                largest = value;
            }
        }
        System.out.println(smallest + ", " + largest); // 1, 5
    }
}

Example usage of MAX_VALUE:

List<Integer> l = Arrays.asList(1, 2, 182938, 1293);
Integer min = Integer.MAX_VALUE;

for (Integer i : l) { 
     min = Math.min(min, i);
}