Since the development of the first personal computers (PCs) more than 30 years
ago, many terms such as bits, bytes, decimal, binary, and hexadecimal have become
part of common language. However, these terms are not always used correctly. This
section helps you understand what these terms and numbering systems mean and
how they relate to the PC technologies you will be studying in future chapters.

Three numbering systems are used in computers: decimal, binary, and hexadecimal.
You already are familiar with the decimal system: Look at your hands. Now, imagine
your fingers are numbered from 0–9, for a total of 10 places. Decimal numbering is
sometimes referred to as base 10.

The binary system doesn’t use your fingers; instead, you count your hands: One
hand represents 0, and the other 1, for a total of two places. Thus, binary numbering
is sometimes referred to as base 2.
The hexadecimal system could be used by a pair of spiders who want to count: One
spider’s legs would be numbered 0–7, and the other spider’s legs would be labeled 8,
9, A–F to reach a total of 16 places. Hexadecimal numbering is sometimes referred
to as base 16.


Decimal Numbering System
We use the decimal or base 10 system for everyday math. A variation on straight
decimal numbering is to use “powers of 2” as a shortcut for large values. For example,
drive storage sizes often are defined in terms of decimal bytes, but the number
of colors that a video card can display can be referred to as “24-bit” (or 224), which
is the same as 16,777,216 colors.

Binary Numbering System
All data is stored in computers in a stream of 1s (on) and 0s (off). Because only two
characters (0 and 1) are used to represent data, this is called a “binary” numbering
system. Text is converted into its numerical equivalents before it is stored, so binary
coding can be used to store all computer data and programs.
Table 1-2 shows how you would count from 1 to 10 (decimal) in binary.


Decimal  0  1    2    3     4      5     6      7      8      9      10
Binary    0  1   10  11 100   101 110  111 1000 1001 1010


Because even a small decimal number occupies many places if expressed in binary,
binary numbers are usually converted into hexadecimal or decimal numbers for
calculations or measurements. Binary numbers are also the basis for bits and bytes:
a single binary value is represented by a bit, and eight bits equals a byte.