What does Binary Mean?

Computers don't do math the same way people do. That isn't to say computers can't do math. They do math very well, but they don't count using the same kind of number system as people. Everyday math, counting and numbering is done with a system called "Base-10." Base-10 means that there are ten possible values for each digit in a number. Any digit can be a zero, or a one, or an eight, or a four, etc.

Binary is a numbering system that represents the same values, but only has two values possible for each digit. Any digit in a binary value can only be a one, or a zero. In Base-10, a value of two is written as "2." In binary, however, a value of two is written as "10."

Suppose we have a two-digit binary number. With two digits, a computer can count to three by incrementing each value as a binary number, starting with both digits at zero which is a value of zero.

A value of one is written as "01"

A value of two is written as "10"

A value of three is written as "11"

To get to four, you need to add a third digit so a value of four is written as "100"

The reason binary is used in computers is because it is a great way to model mathematical expressions using computer circuits. In a computer, a processor circuit can be in one of two states: on or off. By arranging these circuits in series, it becomes possible to store larger and larger values.

If a computer wanted to store a value of 117, it would need a way to store the binary number 01110101. So by setting a series of eight circuits to "off-on-on-on-off-on-off-on," the computer now has the number 117 stored as a single byte.

Since computers can do millions of complex mathematical operations per second, storing long strings of binary values isn't really any problem. For people, however, using binary math would make it a little difficult to figure out how to divide a lunch check.

Those familiar with exponential mathematics might notice rather quickly that binary numbers are simply a list of exponents, or powers of two, read right to left. A good way to read a binary number is to think of each digit from right to left as zero or one, then the number of "twos" in the value, plus the number of "fours" in the value, plus the number of "eights" in the value, and so on.

Or you could save a lot of time and just use hexadecimal.