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Base (mathematics) facts for kids

Kids Encyclopedia Facts

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 23_8. 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:

Decimal (Base 10) Binary (Base 2) Octal (Base 8) Undecimal (Base 11) Hexadecimal (Base 16) Senary (Base 6) Unary (Base 1)
1 1 1 1 1 1 1
2 10 2 2 2 2 11
3 11 3 3 3 3 111
4 100 4 4 4 4 1111
5 101 5 5 5 5 11111
6 110 6 6 6 10 111111
7 111 7 7 7 11 1111111
8 1000 10 8 8 12 11111111
9 1001 11 9 9 13 111111111
10 1010 12 A A 14 1111111111
11 1011 13 10 B 15 11111111111
12 1100 14 11 C 20 111111111111
13 1101 15 12 D 21 1111111111111
14 1110 16 13 E 22 11111111111111
15 1111 17 14 F 23 111111111111111
16 10000 20 15 10 24 1111111111111111

See also

Kids robot.svg In Spanish: Base para niños

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Base (mathematics) Facts for Kids. Kiddle Encyclopedia.