Vigesimal (Base 20) to Hexadecimal (Base 16) Converter
Convert vigesimal numbers to hexadecimal.
CF (base 20) = FF (base 16)
Digits in base 20: 0 to 9 and A to J. Digits in base 16: 0 to 9 and A to F.
How to convert Vigesimal to Hexadecimal
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 16 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 16, 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 16: 0 to 9 and A to F
Worked example 1: 25 from vigesimal to hexadecimal
Step 1: base 20 to decimal25 (base 20) = 2 × 201 + 5 × 200= 40 + 5= 45Step 2: decimal to base 1645 ÷ 16 = 2 remainder 13 (D)2 ÷ 16 = 0 remainder 2Read the remainders from the bottom up: 2D25 (base 20) = 2D (base 16)
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 hexadecimal
Step 1: base 20 to decimalCF (base 20) = 12 × 201 + 15 × 200= 240 + 15= 255Step 2: decimal to base 16255 ÷ 16 = 15 remainder 15 (F)15 ÷ 16 = 0 remainder 15 (F)Read the remainders from the bottom up: FFCF (base 20) = FF (base 16)
Worked example 3: 2A0 from vigesimal to hexadecimal
Step 1: base 20 to decimal2A0 (base 20) = 2 × 202 + 10 × 201= 800 + 200= 1,000Step 2: decimal to base 161,000 ÷ 16 = 62 remainder 862 ÷ 16 = 3 remainder 14 (E)3 ÷ 16 = 0 remainder 3Read the remainders from the bottom up: 3E82A0 (base 20) = 3E8 (base 16)
Need the other direction? Open the Hexadecimal to Vigesimal converter.
Vigesimal to Hexadecimal examples
The decimal number 255 is written CF in vigesimal and FF in hexadecimal.
| Vigesimal | Hexadecimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| F | F | 15 |
| G | 10 | 16 |
| 1C | 20 | 32 |
| 34 | 40 | 64 |
| 50 | 64 | 100 |
| CF | FF | 255 |
| 2A0 | 3E8 | 1000 |
Where Vigesimal to Hexadecimal 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.
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.
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 2 in hexadecimal.
Vigesimal to Hexadecimal FAQ
How do I convert vigesimal to hexadecimal?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 16 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 hexadecimal number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 1.08 hexadecimal digits for every vigesimal digit. The number 255 needs 2 digits in vigesimal and 2 in hexadecimal.
What is CF in hexadecimal?
CF in vigesimal is FF in hexadecimal. 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.