# Base Conversion Tool

Click in either box and type. The conversion is done live.

Can convert negatives and fractional parts too.

Accuracy is about 16 places each side of "."

To convert **between different bases**:

- select the name of the base, and type the number in next to it (this gets converted to decimal)
- change the name of the base

## Bases Greater than 10

What happens when you need more than 10 digits?

## Undecimal (Base 11)

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

Decimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ... |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Undecimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A |
10 | 11 | ... |

## Duodecimal (Base 12)

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

Decimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ... |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Duodecimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A |
B |
10 | 11 | ... |

*(Note: some people use a T for 10 and E for 11, or a "2" and "3" rotated half way around for 10 and 11, but we use the same system as the other bases.)*

## Hexadecimal (Base 16)

Because there are more than 10 digits, hexadecimal is written using letters as well, like this:

Decimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | ... |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Hexadecimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A |
B |
C |
D |
E |
F |
10 | 11 | ... |

## 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:

Decimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | ... |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Vigesimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A |
B |
C |
D |
E |
F |
G |
H |
J |
K |
10 | ... |

## Letters (Base 26)

With "Base 26", you use the letters of the alphabet (not 0 to 9).

Some people start with A=0, B=1, etc. But it seems more natural to use A=1, B=2, etc, as everyone thinks that A is the first letter, B is the second, and so on.

So I use the A=1, B=2, convention, and I use "Z" for Zero! Like this:

Decimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | ... |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Base 26: | Z |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
M |
N |
O |
P |
Q |
R |
S |
T |
U |
V |
W |
X |
Y |
AZ |
AA |
... |

It is fun to use Base 26, type your name in, and see what number you are!

Also, try putting in decimal values after the ".", for example 0.1 produces "BOOO..."