Vigesimal (Base 20) to Ternary (Base 3) Converter
Convert vigesimal numbers to ternary.
CF (base 20) = 100110 (base 3)
Digits in base 20: 0 to 9 and A to J. Digits in base 3: 0 to 2.
How to convert Vigesimal to Ternary
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 3 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 3, 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 3: 0 to 2
Worked example 1: 25 from vigesimal to ternary
Step 1: base 20 to decimal25 (base 20) = 2 × 201 + 5 × 200= 40 + 5= 45Step 2: decimal to base 345 ÷ 3 = 15 remainder 015 ÷ 3 = 5 remainder 05 ÷ 3 = 1 remainder 21 ÷ 3 = 0 remainder 1Read the remainders from the bottom up: 120025 (base 20) = 1200 (base 3)
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 ternary
Step 1: base 20 to decimalCF (base 20) = 12 × 201 + 15 × 200= 240 + 15= 255Step 2: decimal to base 3255 ÷ 3 = 85 remainder 085 ÷ 3 = 28 remainder 128 ÷ 3 = 9 remainder 19 ÷ 3 = 3 remainder 03 ÷ 3 = 1 remainder 01 ÷ 3 = 0 remainder 1Read the remainders from the bottom up: 100110CF (base 20) = 100110 (base 3)
Worked example 3: 2A0 from vigesimal to ternary
Step 1: base 20 to decimal2A0 (base 20) = 2 × 202 + 10 × 201= 800 + 200= 1,000Step 2: decimal to base 31,000 ÷ 3 = 333 remainder 1333 ÷ 3 = 111 remainder 0111 ÷ 3 = 37 remainder 037 ÷ 3 = 12 remainder 112 ÷ 3 = 4 remainder 04 ÷ 3 = 1 remainder 11 ÷ 3 = 0 remainder 1Read the remainders from the bottom up: 11010012A0 (base 20) = 1101001 (base 3)
Need the other direction? Open the Ternary to Vigesimal converter.
Vigesimal to Ternary examples
The decimal number 255 is written CF in vigesimal and 100110 in ternary.
| Vigesimal | Ternary | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 21 | 7 |
| 8 | 22 | 8 |
| A | 101 | 10 |
| F | 120 | 15 |
| G | 121 | 16 |
| 1C | 1012 | 32 |
| 34 | 2101 | 64 |
| 50 | 10201 | 100 |
| CF | 100110 | 255 |
| 2A0 | 1101001 | 1000 |
Where Vigesimal to Ternary 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.
Ternary uses the digits 0, 1 and 2, and each ternary digit (a trit) carries about 1.58 bits of information. Ternary is rare in real hardware, though the Soviet Setun computer of 1958 used a balanced ternary design. Today it shows up mostly in computer science courses and puzzles.
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 6 in ternary.
Vigesimal to Ternary FAQ
How do I convert vigesimal to ternary?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 3 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 ternary number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 2.73 ternary digits for every vigesimal digit. The number 255 needs 2 digits in vigesimal and 6 in ternary.
What is CF in ternary?
CF in vigesimal is 100110 in ternary. 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.