Binary to Base-12 Converter
Convert binary integers to base-12 (duodecimal) instantly. Enter a binary number such as 11001 to get its decimal value, repeated division by 12, exact base-12 result, and conversion steps.
What Is Binary to Base-12 Conversion?
Binary to base-12 conversion changes a number written in base 2 into the equivalent value in base 12. Base 12 is also called the duodecimal numeral system.
Binary uses only 0 and 1, while base 12 uses
0–9 plus two extra digits:
How to Convert Binary to Base-12
1. Validate Binary Input
Make sure the number contains only binary digits 0 and 1.
2. Find the Decimal Value
Evaluate the binary number using powers of 2.
3. Divide by 12
Divide the decimal value by 12 and record the remainder.
4. Repeat
Continue dividing each quotient by 12 until the quotient is zero.
5. Convert Remainders
Remainder 10 becomes A and remainder 11 becomes B.
6. Reverse the Digits
Read the remainder sequence from last to first.
Base-12 Digit Table
| Decimal | Base-12 Digit |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 8 |
| 9 | 9 |
| 10 | A |
| 11 | B |
Example: Convert Binary 1010 to Base-12
Example: Convert Binary 1011 to Base-12
Example: Convert Binary 11001 to Base-12
Binary to Base-12 Conversion Table
| Binary | Decimal | Base-12 |
|---|---|---|
0 | 0 | 0 |
1 | 1 | 1 |
10 | 2 | 2 |
11 | 3 | 3 |
100 | 4 | 4 |
101 | 5 | 5 |
110 | 6 | 6 |
111 | 7 | 7 |
1000 | 8 | 8 |
1001 | 9 | 9 |
1010 | 10 | A |
1011 | 11 | B |
1100 | 12 | 10 |
1101 | 13 | 11 |
1110 | 14 | 12 |
1111 | 15 | 13 |
11000 | 24 | 20 |
11001 | 25 | 21 |
What Is Base 12?
Base 12 uses twelve digit values. With the notation used by this converter, the digit set is:
The place values are powers of 12:
Binary vs Base-12
| Feature | Binary | Base-12 |
|---|---|---|
| Base | 2 | 12 |
| Digits | 0, 1 | 0–9, A, B |
| Place Values | Powers of 2 | Powers of 12 |
| Decimal 10 | 1010 |
A |
| Decimal 11 | 1011 |
B |
| Decimal 25 | 11001 |
21 |
Why Can’t Binary Be Grouped Directly Into Base-12?
Direct bit grouping works when the destination base is a power of 2. For example, binary can be grouped directly for base 4, base 8, or base 16.
Base 12 is not a power of 2, so there is no fixed group of binary bits that corresponds exactly to one base-12 digit.
Common Binary to Base-12 Mistakes
Using Invalid Binary Digits
The input may contain only 0 and 1.
Forgetting A and B
Base-12 values 10 and 11 are represented as A and B in this calculator.
Reading Remainders Forward
Repeated-division remainders must be read from last to first.
Trying Fixed Binary Groups
Base 12 is not a power of 2, so direct binary grouping is not valid.
Related BinaryCon Tools
Binary to Base-12 Converter FAQs
How do you convert binary to base 12?
What is binary 1010 in base 12?
1010 equals decimal 10, represented as
A in this base-12 notation.
What is binary 1011 in base 12?
1011 equals decimal 11, represented as
B in base 12.
What is binary 1100 in base 12?
1100 equals decimal 12, which is
10₁₂.
What is binary 11001 in base 12?
11001 equals decimal 25, which is
21₁₂.