Base 32 to Vigesimal (Base 20) Converter
Convert base 32 numbers to vigesimal.
7V (base 32) = CF (base 20)
Digits in base 32: 0 to 9 and A to V. Digits in base 20: 0 to 9 and A to J.
How to convert Base 32 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 32 the place values, from the right, are 320 = 1, 321 = 32, 322 = 1024 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 32 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 32: 1, 32, 1024, 32768, 1048576, 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 32: 0 to 9 and A to Vdigits in base 20: 0 to 9 and A to J
Worked example 1: 1D from base 32 to vigesimal
Step 1: base 32 to decimal1D (base 32) = 1 × 321 + 13 × 320= 32 + 13= 45Step 2: decimal to base 2045 ÷ 20 = 2 remainder 52 ÷ 20 = 0 remainder 2Read the remainders from the bottom up: 251D (base 32) = 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: 7V from base 32 to vigesimal
Step 1: base 32 to decimal7V (base 32) = 7 × 321 + 31 × 320= 224 + 31= 255Step 2: decimal to base 20255 ÷ 20 = 12 remainder 15 (F)12 ÷ 20 = 0 remainder 12 (C)Read the remainders from the bottom up: CF7V (base 32) = CF (base 20)
Worked example 3: V8 from base 32 to vigesimal
Step 1: base 32 to decimalV8 (base 32) = 31 × 321 + 8 × 320= 992 + 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: 2A0V8 (base 32) = 2A0 (base 20)
Need the other direction? Open the Vigesimal to Base 32 converter.
Base 32 to Vigesimal examples
The decimal number 255 is written 7V in base 32 and CF in vigesimal.
| Base 32 | Vigesimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 7 | 7 | 7 |
| 8 | 8 | 8 |
| A | A | 10 |
| F | F | 15 |
| G | G | 16 |
| 10 | 1C | 32 |
| 20 | 34 | 64 |
| 34 | 50 | 100 |
| 7V | CF | 255 |
| V8 | 2A0 | 1000 |
Where Base 32 to Vigesimal comes up
Base 32 here uses 0 to 9 and A to V, and each digit stands for exactly five bits. It is handy for compact IDs. The text encodings called Base32 in RFC 4648 work on bytes and use their own alphabets, so their output is not the same as converting a whole number.
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 smaller base spreads the same value over more digits, so the result is longer. The number 255 needs 2 digits in base 32 and 2 in vigesimal.
Base 32 to Vigesimal FAQ
How do I convert base 32 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 base 32 use?
Base 32 uses the digits 0 to 9 and A to V. For example, W is not a valid digit in base 32. Letters are not case sensitive on this converter, and results are shown in capitals.
Will the vigesimal number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 1.16 vigesimal digits for every base 32 digit. The number 255 needs 2 digits in base 32 and 2 in vigesimal.
What is 7V in vigesimal?
7V in base 32 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.