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

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):

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:

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

If Dogs ruled the world they might use base-8 instead of decimal:

0   1   2   3   4   5   6   7

Nonary (Base 9) has 9 digits:

0   1   2   3   4   5   6   7   8

We count like this:

Decimal (Base 10) has 10 digits:

0   1   2   3   4   5   6   7   8   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:

Hexadecimal (Base 16)

Dogs might understand hexadecimal well.

It uses the digits 0 to 9, then the six letters A to F, 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:

Sexagesimal (Base 60)

Sexagesimal works like clockwork!

There are no special codes, just the numbers 0 to 59, like we use with hours and minutes.

The main advantage is that 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, which makes it easy for us to divide up hours and minutes.

More About Bases

How to Show the Base

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

101₂
This shows that is in Base 2 (Binary)

314₈
This shows that is in Base 8 (Octal)