Count in Different Bases

A number system is a set of rules for writing numbers. Throughout history, people have used many different number systems, including tally marks, Chinese numerals, and Roman numerals. A positional number system is a number system where the position of a digit has value. Today most people count and do arithmetic in a positional number system called base 10. It is called base 10 because the number system has ten symbols. In most countries and languages today, those ten symbols are the Arabic numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Humans probably started counting and doing arithmetic in base 10 because we have ten fingers.

It is possible to count and do arithmetic in other bases. Some ancient communities counted in base 5 and others in base 20, meaning their number system had only five symbols or twenty symbols, respectively. Computers count and perform arithmetic in base 2 because internally computers are composed of billions of tiny two-state electronic circuits. Each circuit may be either off or on, electric current not flowing or flowing. These two states represent two symbols: 0 and 1, so computers use base 2. The table below will help you practice counting in different bases.

Count vertically from to in three bases.

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Futher Reading

If you want to learn more about base 2 and how computers use it to perform calculations, check out the book Really Understand Binary.