The number system that you are probably most familiar with is the
decimal, or base 10, number system.
When representing a number using decimal notation, each position in the number corresponds to a power of 10, and each digit of the number can be one of the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
For example, the decimal number 6437 represents the sum:
6 * 10^{3} + 4 * 10^{2} + 3 * 10^{1} + 7 * 10^{0}
or
6 * 1000 + 4 * 100 + 3 * 10 + 7 * 1
Because computers store data as a sequence of switches that can be either on or off, they use a base 2 number system referred to as the
binary number system.
In this number system, each position in a number corresponds to a power of 2, and each digit can be either the
binary digit 1 or 0. For example, the binary number 110101 represents the following sum, which is equal to 45 in the decimal number
system:
1 * 2
^{5} + 1 * 2
^{4} + 0 * 2
^{3} + 1 * 2
^{2} + 0 * 2
^{1} + 1 * 2
^{0} or
1 * 32 + 1 * 16 + 0 * 8 + 1 * 4 + 0 * 2 + 1 * 1
The expression "binary digit" meaning a 1 or a 0 is usually referred to as a bit. Figure A-2 shows the decimal number 2001 expressed in binary, octal, decimal, and hexadecimal form. The number 7B9 is obviously hexadecimal, because the symbol B can only occur in hexadecimal numbers. However, the number 111 might be in any of the four number systems discussed. To avoid ambiguity, people use a subscript of 2, 8, 10, or 16 to indicate the radix when it is not obvious from the context.