Number Bases

Base 10
We use "Base 10" every day ... it is our Decimal Number System.

It has 10 digits:

0   1   2   3   4   5   6   7   8   9

We count like this: But there are other bases!

Binary (Base 2) has only 2 digits: 0 and 1
We count like this: See how it is done in this little demonstration (press play):

Base:

Hexadecimal

Decimal

Binary

0

128 = 27

0

64 = 26

0

32 = 25

0

16 = 24

0

8 = 23

0

4 = 22

0

2 = 21

0

1 = 20

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Also try Decimal, and try other bases like 3 or 4. It will help you understand how all these different bases work.

Ternary (Base 3) has 3 digits: 0, 1 and 2
We count like this:

Quaternary (Base 4) has 4 digits: 0, 1, 2 and 3
We count like this:

Quinary (Base 5) has 5 digits: 0, 1, 2, 3 and 4
We count like this:

Senary (Base 6) has 6 digits: 0, 1, 2, 3, 4 and 5
We count like this:

Septenary (Base 7) has 7 digits: 0, 1, 2, 3, 4 5 and 6
We count like this:

Octal (Base 8) has 8 digits: 0, 1, 2, 3, 4, 5, 6 and 7
We count like this:

Nonary (Base 9) has 9 digits: 0, 1, 2, 3, 4, 5, 6, 7 and 8
We count like this:

Decimal (Base 10) has 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9
Well ... we talked about this at the start but here it is again:

Undecimal (Base 11)
Undecimal (Base 11) needs one more digit than Decimal, so "A" is used, like this:

Duodecimal (Base 12)
Duodecimal (Base 12) needs two more digits than Decimal, so "A" and "B" are used:

Tridecimal (Base 13)
Tridecimal (Base 13) needs three more digits than Decimal, so "Z" "Y" and "X" are used:

Hexadecimal (Base 16)
Because there are more than 10 digits, hexadecimal is written using letters as well, like this:

Vigesimal (Base 20)
With vigesimal, the convention is that I is not used because it looks like 1, so J=18 and K=19, as in this table:

More About Bases
Note: the Number Base is also called the Radix

How to Show the Base
To show what base a number has, put the base in the lower right like this:

101 2 This shows that is in Base 2 (Binary)

314 8 This shows that is in Base 8 (Octal)