Vigesimal (Base 20) to Binary (Base 2) Converter
Convert vigesimal numbers to binary.
CF (base 20) = 11111111 (base 2)
Digits in base 20: 0 to 9 and A to J. Digits in base 2: 0 and 1.
How to convert Vigesimal to Binary
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 2 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 2, 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 2: 0 and 1
Worked example 1: 25 from vigesimal to binary
Step 1: base 20 to decimal25 (base 20) = 2 × 201 + 5 × 200= 40 + 5= 45Step 2: decimal to base 245 ÷ 2 = 22 remainder 122 ÷ 2 = 11 remainder 011 ÷ 2 = 5 remainder 15 ÷ 2 = 2 remainder 12 ÷ 2 = 1 remainder 01 ÷ 2 = 0 remainder 1Read the remainders from the bottom up: 10110125 (base 20) = 101101 (base 2)
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 binary
Step 1: base 20 to decimalCF (base 20) = 12 × 201 + 15 × 200= 240 + 15= 255Step 2: decimal to base 2255 ÷ 2 = 127 remainder 1127 ÷ 2 = 63 remainder 163 ÷ 2 = 31 remainder 131 ÷ 2 = 15 remainder 115 ÷ 2 = 7 remainder 17 ÷ 2 = 3 remainder 13 ÷ 2 = 1 remainder 11 ÷ 2 = 0 remainder 1Read the remainders from the bottom up: 11111111CF (base 20) = 11111111 (base 2)
Worked example 3: 2A0 from vigesimal to binary
Step 1: base 20 to decimal2A0 (base 20) = 2 × 202 + 10 × 201= 800 + 200= 1,000Step 2: decimal to base 21,000 ÷ 2 = 500 remainder 0500 ÷ 2 = 250 remainder 0250 ÷ 2 = 125 remainder 0125 ÷ 2 = 62 remainder 162 ÷ 2 = 31 remainder 031 ÷ 2 = 15 remainder 115 ÷ 2 = 7 remainder 17 ÷ 2 = 3 remainder 13 ÷ 2 = 1 remainder 11 ÷ 2 = 0 remainder 1Read the remainders from the bottom up: 11111010002A0 (base 20) = 1111101000 (base 2)
Need the other direction? Open the Binary to Vigesimal converter.
Vigesimal to Binary examples
The decimal number 255 is written CF in vigesimal and 11111111 in binary.
| Vigesimal | Binary | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 10 | 2 |
| 7 | 111 | 7 |
| 8 | 1000 | 8 |
| A | 1010 | 10 |
| F | 1111 | 15 |
| G | 10000 | 16 |
| 1C | 100000 | 32 |
| 34 | 1000000 | 64 |
| 50 | 1100100 | 100 |
| CF | 11111111 | 255 |
| 2A0 | 1111101000 | 1000 |
Where Vigesimal to Binary 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.
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.
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 8 in binary.
Vigesimal to Binary FAQ
How do I convert vigesimal to binary?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 2 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 binary number be longer or shorter?
Longer. Going to a smaller base spreads the same value over more digits, so the result is longer. Roughly 4.32 binary digits for every vigesimal digit. The number 255 needs 2 digits in vigesimal and 8 in binary.
What is CF in binary?
CF in vigesimal is 11111111 in binary. 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.