Base (mathematics) facts for kids

A base or radix is a special number in mathematics. It tells us how many different digits a counting system uses to show numbers. Think of it like the alphabet for numbers!

The most common base we use every day is the decimal system. "Dec" means 10, so it uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Many people believe we use base 10 because we have 10 fingers.

A base is usually a whole number bigger than 1. Sometimes, you might see a small number written next to a number, like . This means "23 in base 8." In our usual base 10, this number would be 19.

Bases in Computers

Computers use different bases to work with numbers.

Binary (Base 2)

Computers mostly use binary, which is base 2. This is because computers work with very simple signals: they are either "on" (represented by 1) or "off" (represented by 0). So, binary only uses two digits: 0 and 1.

Hexadecimal (Base 16)

Hexadecimal (base 16) is also used in computers. It's helpful because it groups binary digits together. Every four binary digits can be shown as one hexadecimal digit. Since base 16 needs more than 10 digits, it uses letters for the numbers after 9: A, B, C, D, E, and F.

Counting in Different Ways

Some very old ways of counting used base one. Imagine making a mark on a wall for every item you count – that's like unary counting!

Some old measurement systems used base twelve, also called duodecimal. You can still see this in English words like "dozen" (which means 12) and "gross" (which is 144, or 12 times 12). Also, a "foot" is 12 inches.

Even angle measurements often use a system that came from the Babylonian numerals, which used base 60.

Numbers in Different Bases

Here are some examples of how numbers look in different bases, compared to our usual base 10:

See also

In Spanish: Base para niños