Duodecimal (Base 12) to Vigesimal (Base 20) Converter
Convert duodecimal numbers to vigesimal.
193 (base 12) = CF (base 20)
Digits in base 12: 0 to 9 and A to B. Digits in base 20: 0 to 9 and A to J.
How to convert Duodecimal to Vigesimal
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 12 the place values, from the right, are 120 = 1, 121 = 12, 122 = 144 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 12 number into decimal, then divide by 20 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 12: 1, 12, 144, 1728, 20736, and so ondivide by 20, keep the remainder, repeat until the quotient is 0the answer is the remainders read from last to firstdigits in base 12: 0 to 9 and A to Bdigits in base 20: 0 to 9 and A to J
Worked example 1: 39 from duodecimal to vigesimal
Step 1: base 12 to decimal39 (base 12) = 3 × 121 + 9 × 120= 36 + 9= 45Step 2: decimal to base 2045 ÷ 20 = 2 remainder 52 ÷ 20 = 0 remainder 2Read the remainders from the bottom up: 2539 (base 12) = 25 (base 20)
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: 193 from duodecimal to vigesimal
Step 1: base 12 to decimal193 (base 12) = 1 × 122 + 9 × 121 + 3 × 120= 144 + 108 + 3= 255Step 2: decimal to base 20255 ÷ 20 = 12 remainder 15 (F)12 ÷ 20 = 0 remainder 12 (C)Read the remainders from the bottom up: CF193 (base 12) = CF (base 20)
Worked example 3: 6B4 from duodecimal to vigesimal
Step 1: base 12 to decimal6B4 (base 12) = 6 × 122 + 11 × 121 + 4 × 120= 864 + 132 + 4= 1,000Step 2: decimal to base 201,000 ÷ 20 = 50 remainder 050 ÷ 20 = 2 remainder 10 (A)2 ÷ 20 = 0 remainder 2Read the remainders from the bottom up: 2A06B4 (base 12) = 2A0 (base 20)
Need the other direction? Open the Vigesimal to Duodecimal converter.
Duodecimal to Vigesimal examples
The decimal number 255 is written 193 in duodecimal and CF in vigesimal.
| Duodecimal | Vigesimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| 13 | F | 15 |
| 14 | G | 16 |
| 28 | 1C | 32 |
| 54 | 34 | 64 |
| 84 | 50 | 100 |
| 193 | CF | 255 |
| 6B4 | 2A0 | 1000 |
Where Duodecimal to Vigesimal comes up
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.
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.
Going to a larger base packs more value into each digit, so the result is shorter. The number 255 needs 3 digits in duodecimal and 2 in vigesimal.
Duodecimal to Vigesimal FAQ
How do I convert duodecimal to vigesimal?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 20 repeatedly and read the remainders from last to first.
Which digits does duodecimal use?
Base 12 uses the digits 0 to 9 and A to B. For example, C is not a valid digit in base 12. Letters are not case sensitive on this converter, and results are shown in capitals.
Will the vigesimal number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.83 vigesimal digits for every duodecimal digit. The number 255 needs 3 digits in duodecimal and 2 in vigesimal.
What is 193 in vigesimal?
193 in duodecimal is CF in vigesimal. 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.