Hexadecimal (Base 16) to Vigesimal (Base 20) Converter
Convert hexadecimal numbers to vigesimal.
FF (base 16) = CF (base 20)
Digits in base 16: 0 to 9 and A to F. Digits in base 20: 0 to 9 and A to J.
How to convert Hexadecimal 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 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 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 16: 1, 16, 256, 4096, 65536, 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 16: 0 to 9 and A to Fdigits in base 20: 0 to 9 and A to J
Worked example 1: 2D from hexadecimal to vigesimal
Step 1: base 16 to decimal2D (base 16) = 2 × 161 + 13 × 160= 32 + 13= 45Step 2: decimal to base 2045 ÷ 20 = 2 remainder 52 ÷ 20 = 0 remainder 2Read the remainders from the bottom up: 252D (base 16) = 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: FF from hexadecimal to vigesimal
Step 1: base 16 to decimalFF (base 16) = 15 × 161 + 15 × 160= 240 + 15= 255Step 2: decimal to base 20255 ÷ 20 = 12 remainder 15 (F)12 ÷ 20 = 0 remainder 12 (C)Read the remainders from the bottom up: CFFF (base 16) = CF (base 20)
Worked example 3: 3E8 from hexadecimal to vigesimal
Step 1: base 16 to decimal3E8 (base 16) = 3 × 162 + 14 × 161 + 8 × 160= 768 + 224 + 8= 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: 2A03E8 (base 16) = 2A0 (base 20)
Need the other direction? Open the Vigesimal to Hexadecimal converter.
Hexadecimal to Vigesimal examples
The decimal number 255 is written FF in hexadecimal and CF in vigesimal.
| Hexadecimal | Vigesimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| F | F | 15 |
| 10 | G | 16 |
| 20 | 1C | 32 |
| 40 | 34 | 64 |
| 64 | 50 | 100 |
| FF | CF | 255 |
| 3E8 | 2A0 | 1000 |
Where Hexadecimal to Vigesimal 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.
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 2 digits in hexadecimal and 2 in vigesimal.
Hexadecimal to Vigesimal FAQ
How do I convert hexadecimal 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 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 vigesimal number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.93 vigesimal digits for every hexadecimal digit. The number 255 needs 2 digits in hexadecimal and 2 in vigesimal.
What is FF in vigesimal?
FF in hexadecimal 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.