Hexadecimal (Base 16) to Duodecimal (Base 12) Converter
Convert hexadecimal numbers to duodecimal.
FF (base 16) = 193 (base 12)
Digits in base 16: 0 to 9 and A to F. Digits in base 12: 0 to 9 and A to B.
How to convert Hexadecimal to Duodecimal
Every positional number system works the same way: a digit is worth its own value times the base raised to the power of its position. In base 16 the place values, from the right, are 160 = 1, 161 = 16, 162 = 256 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 16 number into decimal, then divide by 12 and read the remainders from the bottom up. Two short steps, and you can check the number in the middle.
The method
decimal value = each digit × its place value, all added upplace values in base 16: 1, 16, 256, 4096, 65536, and so ondivide by 12, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to firstdigits in base 16: 0 to 9 and A to Fdigits in base 12: 0 to 9 and A to B
Worked example 1: 2D from hexadecimal to duodecimal
Step 1: base 16 to decimal2D (base 16) = 2 × 161 + 13 × 160= 32 + 13= 45Step 2: decimal to base 1245 ÷ 12 = 3 remainder 93 ÷ 12 = 0 remainder 3Read the remainders from the bottom up: 392D (base 16) = 39 (base 12)
Letters stand for values from 10 up: A = 10, B = 11, C = 12 and so on. Remainders come out last digit first, which is why you read them from the bottom up. Digits that are 0 add nothing to the sum, so they are left out of the expansion.
Worked example 2: FF from hexadecimal to duodecimal
Step 1: base 16 to decimalFF (base 16) = 15 × 161 + 15 × 160= 240 + 15= 255Step 2: decimal to base 12255 ÷ 12 = 21 remainder 321 ÷ 12 = 1 remainder 91 ÷ 12 = 0 remainder 1Read the remainders from the bottom up: 193FF (base 16) = 193 (base 12)
Worked example 3: 3E8 from hexadecimal to duodecimal
Step 1: base 16 to decimal3E8 (base 16) = 3 × 162 + 14 × 161 + 8 × 160= 768 + 224 + 8= 1,000Step 2: decimal to base 121,000 ÷ 12 = 83 remainder 483 ÷ 12 = 6 remainder 11 (B)6 ÷ 12 = 0 remainder 6Read the remainders from the bottom up: 6B43E8 (base 16) = 6B4 (base 12)
Need the other direction? Open the Duodecimal to Hexadecimal converter.
Hexadecimal to Duodecimal examples
The decimal number 255 is written FF in hexadecimal and 193 in duodecimal.
| Hexadecimal | Duodecimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| F | 13 | 15 |
| 10 | 14 | 16 |
| 20 | 28 | 32 |
| 40 | 54 | 64 |
| 64 | 84 | 100 |
| FF | 193 | 255 |
| 3E8 | 6B4 | 1000 |
Where Hexadecimal to Duodecimal comes up
Hexadecimal (base 16) uses 0 to 9 and A to F, and each hex digit stands for exactly four bits, so one byte is always two hex digits. You see it in web colours like #FF8800, memory addresses, MAC addresses, hash values and byte dumps.
Duodecimal (base 12) uses 0 to 9 plus A for ten and B for eleven. Twelve divides evenly by 2, 3, 4 and 6. That is why dozens, the 12-hour clock, twelve inches to a foot and twelve months feel natural. A few mathematicians even argue it is a better base than ten.
Going to a smaller base spreads the same value over more digits, so the result is longer. The number 255 needs 2 digits in hexadecimal and 3 in duodecimal.
Hexadecimal to Duodecimal FAQ
How do I convert hexadecimal to duodecimal?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 12 repeatedly and read the remainders from last to first.
Which digits does hexadecimal use?
Base 16 uses the digits 0 to 9 and A to F. For example, G is not a valid digit in base 16. Letters are not case sensitive on this converter, and results are shown in capitals.
Will the duodecimal number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 1.12 duodecimal digits for every hexadecimal digit. The number 255 needs 2 digits in hexadecimal and 3 in duodecimal.
What is FF in duodecimal?
FF in hexadecimal is 193 in duodecimal. Both are the decimal number 255.
Can I convert negative numbers or fractions?
The converter handles whole numbers, and a leading minus sign works for negatives. Fractions use a different method, where you repeatedly multiply the fractional part by the new base, and they are not supported here.