Binary (Base 2) to Vigesimal (Base 20) Converter
Convert binary numbers to vigesimal.
11111111 (base 2) = CF (base 20)
Digits in base 2: 0 and 1. Digits in base 20: 0 to 9 and A to J.
How to convert Binary 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 2 the place values, from the right, are 20 = 1, 21 = 2, 22 = 4 and so on.
Most pairs have no direct trick, so go through decimal, the base we all calculate in. First turn the base 2 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 2: 1, 2, 4, 8, 16, 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 2: 0 and 1digits in base 20: 0 to 9 and A to J
Worked example 1: 101101 from binary to vigesimal
Step 1: base 2 to decimal101101 (base 2) = 1 × 25 + 1 × 23 + 1 × 22 + 1 × 20= 32 + 8 + 4 + 1= 45Step 2: decimal to base 2045 ÷ 20 = 2 remainder 52 ÷ 20 = 0 remainder 2Read the remainders from the bottom up: 25101101 (base 2) = 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: 11111111 from binary to vigesimal
Step 1: base 2 to decimal11111111 (base 2) = 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20= 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1= 255Step 2: decimal to base 20255 ÷ 20 = 12 remainder 15 (F)12 ÷ 20 = 0 remainder 12 (C)Read the remainders from the bottom up: CF11111111 (base 2) = CF (base 20)
Worked example 3: 1111101000 from binary to vigesimal
Step 1: base 2 to decimal1111101000 (base 2) = 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 23= 512 + 256 + 128 + 64 + 32 + 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: 2A01111101000 (base 2) = 2A0 (base 20)
Need the other direction? Open the Vigesimal to Binary converter.
Binary to Vigesimal examples
The decimal number 255 is written 11111111 in binary and CF in vigesimal.
| Binary | Vigesimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 10 | 2 | 2 |
| 111 | 7 | 7 |
| 1000 | 8 | 8 |
| 1010 | A | 10 |
| 1111 | F | 15 |
| 10000 | G | 16 |
| 100000 | 1C | 32 |
| 1000000 | 34 | 64 |
| 1100100 | 50 | 100 |
| 11111111 | CF | 255 |
| 1111101000 | 2A0 | 1000 |
Where Binary to Vigesimal comes up
Binary uses only 0 and 1, because a digital circuit has two stable states: off and on. Every number a computer stores is binary underneath. You meet it when you work with bit flags, bit masks, subnet masks and low-level debugging.
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 8 digits in binary and 2 in vigesimal.
Binary to Vigesimal FAQ
How do I convert binary 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 binary use?
Base 2 uses the digits 0 and 1. For example, 2 is not a valid digit in base 2.
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 0.23 vigesimal digits for every binary digit. The number 255 needs 8 digits in binary and 2 in vigesimal.
What is 11111111 in vigesimal?
11111111 in binary 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.