Introduction to Binary Numbers

How Computers Store Numbers

Computer systems are constructed of digital electronics. That means that their electronic circuits can exist in only one of two states: on or off. Most computer electronics use voltage levels to indicate their present state. For example, a transistor with five volts would be considered "on", while a transistor with no voltage would be considered "off." Not all computer hardware uses voltage, however. CD-ROM's, for example, use microscopic dark spots on the surface of the disk to indicate "off," while the ordinary shiny surface is considered "on." Hard disks use magnetism, while computer memory uses electric charges stored in tiny capacitors to indicate "on" or "off."

These patterns of "on" and "off" stored inside the computer are used to encode numbers using the binary number system. The binary number system is a method of storing ordinary numbers such as 42 or 365 as patterns of 1's and 0's. Because of their digital nature, a computer's electronics can easily manipulate numbers stored in binary by treating 1 as "on" and 0 as "off." Computers have circuits that can add, subtract, multiply, divide, and do many other things to numbers stored in binary.

How Binary Works

The decimal number system that people use every day contains ten digits, 0 through 9. Start counting in decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, Oops! There are no more digits left. How do we continue counting with only ten digits? We add a second column of digits, worth ten times the value of the first column. Start counting again: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 (Note that the right column goes back to zero here.), 21, 22, 23, ... , 94, 95, 96, 97, 98, 99, Oops! Once again, there are no more digits left. The only way to continue counting is to add yet another column worth ten times as much as the one before. Continue