In everyday life, we use the base 10 (decimal) number system, which consists of ten digits from 0 to 9. This system is familiar to us for counting, arithmetic, and most of our daily numerical tasks. However, in computer science and various technical fields, different base systems are frequently used due to their unique properties and applications.
Base 2 (binary) is the foundation of all modern computing systems. It uses only two digits, 0 and 1, representing the two states of a digital circuit: off and on. Binary is crucial for computer operations, data storage, and processing.
Base 8 (octal) and base 16 (hexadecimal) are also commonly used in computing. Octal uses digits from 0 to 7 and is capable of representing three binary digits (bits) in a more compact form. Hexadecimal, which uses digits from 0 to 9 and letters A to F, can represent four binary digits. Because there are eight bits in a byte, a byte can be represented by just two hexadecimal digits, as opposed to eight binary digits. This increases readability and reduces the likelihood of errors due to the more concise and varied character set.
The table below displays the conversions of numbers from base 10 to bases 1 through 36. The "Value" column is in base 10, while the other columns show the equivalent values in different bases.