Vigesimal (Base 20) to Duodecimal (Base 12) Converter
Convert vigesimal numbers to duodecimal.
CF (base 20) = 193 (base 12)
Digits in base 20: 0 to 9 and A to J. Digits in base 12: 0 to 9 and A to B.
How to convert Vigesimal 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 20 the place values, from the right, are 200 = 1, 201 = 20, 202 = 400 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 20 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 20: 1, 20, 400, 8000, 160000, 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 20: 0 to 9 and A to Jdigits in base 12: 0 to 9 and A to B
Worked example 1: 25 from vigesimal to duodecimal
Step 1: base 20 to decimal25 (base 20) = 2 × 201 + 5 × 200= 40 + 5= 45Step 2: decimal to base 1245 ÷ 12 = 3 remainder 93 ÷ 12 = 0 remainder 3Read the remainders from the bottom up: 3925 (base 20) = 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: CF from vigesimal to duodecimal
Step 1: base 20 to decimalCF (base 20) = 12 × 201 + 15 × 200= 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: 193CF (base 20) = 193 (base 12)
Worked example 3: 2A0 from vigesimal to duodecimal
Step 1: base 20 to decimal2A0 (base 20) = 2 × 202 + 10 × 201= 800 + 200= 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: 6B42A0 (base 20) = 6B4 (base 12)
Need the other direction? Open the Duodecimal to Vigesimal converter.
Vigesimal to Duodecimal examples
The decimal number 255 is written CF in vigesimal and 193 in duodecimal.
| Vigesimal | Duodecimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| F | 13 | 15 |
| G | 14 | 16 |
| 1C | 28 | 32 |
| 34 | 54 | 64 |
| 50 | 84 | 100 |
| CF | 193 | 255 |
| 2A0 | 6B4 | 1000 |
Where Vigesimal to Duodecimal comes up
Vigesimal counts in twenties, with the digits 0 to 9 and A to J. The Maya wrote numbers in a base 20 system, and French still says quatre-vingts, four twenties, for 80.
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 vigesimal and 3 in duodecimal.
Vigesimal to Duodecimal FAQ
How do I convert vigesimal 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 vigesimal use?
Base 20 uses the digits 0 to 9 and A to J. For example, K is not a valid digit in base 20. 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 1.21 duodecimal digits for every vigesimal digit. The number 255 needs 2 digits in vigesimal and 3 in duodecimal.
What is CF in duodecimal?
CF in vigesimal 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.