# Binary

**Binary** is base 2 number system. It is base 2 because it uses two possible numbers: 0 and 1. Decimal, the system most of the world uses for daily life, is a base 10 system – it uses 10 characters (0–9). When binary numbers are written, a subscript "(2)" is added to distinguish them from the same number in base 10.

Computers work in binary, because wires can store information in two different ways: by being powered, or not being powered. Sets of binary numbers can be used to represent any information, such as text, audio, or video.

## Number system

When being introduced to binary numbers, it helps to go back and think about how base 10 or decimal numbers work. Consider the number 1101_{(10)} (base 10). We identify this number as one-thousand, one-hundred, one because it has a 1 in the thousands place, a 1 in the hundreds place, and a 1 in the ones place. But since the places represent 8, 4, 2, and 1 in binary, instead of 1000, 100, 10, and 1, the value converted to decimal (base 10) would be 8 + 4 + 1 = 13_{(10)}.

For another example, the binary number 101_{(2)} is 5 in decimal. The bit on the right is 1 and has a value of 1 (2^0). The middle bit has a value of 2 (2^1 or just 2), but it is a 0, so it is not added. The bit on the left is 1 and has a value of 4 (2^2 or 2 * 2). The bits that are 1s have values of 1 and 4. 1 + 4 = **5**.

## Computers

All computers use binary at the lowest level. Most hard memory, like compact discs and DVDs, use binary to represent large files.

With computers, eight binary bits together is called a *byte*. The size of files is commonly measured in *kilobytes* or *megabytes* (sometimes in *gigabytes*). A kilobyte is 1000 bytes. A megabyte is 1000 kilobytes, a gigabyte is 1000 megabytes and a terabyte is 1000 gigabytes. Sometimes, it is easier to measure bytes in groups of 1024, since 1024 is a power of 2. There are 1024 bytes in a *kibibyte*, 1024 kibibytes in a *mebibyte*, and 1024 mebibytes in a *gibibyte*.

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**Categories:** Computer science | Mathematics | Encodings

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