As you can see from the previous post, binary numbers can become rather long. With only two possible values, 0 and 1, it takes 16 binary digits to represent the decimal value +32,768. For that reason, the hexadecimal, or base 16, system is often used as a shorthand representation of binary numbers. The hexadecimal system uses 16 digits: 0 to 9 and A to F. The letters A to F represent the values 10, 11, 12, 13, 14, and 15.

The maximum value that can be represented in four binary digits is 2⁴ − 1, or 15. The maximum value of a hexadecimal digit is also 15, which is represented by the letter F. So you can reduce the size of a binary number by using hexadecimal digits to represent each group of four binary digits.

Here are displayed the hexadecimal digits along with their binary equivalents.

To represent the following binary number in hexadecimal, you simply substitute the appropriate hex digit for each set of four binary digits.

Here’s an interesting sequence of hexadecimal numbers. The first 32 bits of every Java applet are:

Translated into hexadecimal, that binary number becomes:

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