Binary (Base 2) to Duodecimal (Base 12) Converter
Convert binary numbers to duodecimal.
11111111 (base 2) = 193 (base 12)
Digits in base 2: 0 and 1. Digits in base 12: 0 to 9 and A to B.
How to convert Binary to Duodecimal
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 12 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 12, 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 12: 0 to 9 and A to B
Worked example 1: 101101 from binary to duodecimal
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 1245 ÷ 12 = 3 remainder 93 ÷ 12 = 0 remainder 3Read the remainders from the bottom up: 39101101 (base 2) = 39 (base 12)
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 duodecimal
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 12255 ÷ 12 = 21 remainder 321 ÷ 12 = 1 remainder 91 ÷ 12 = 0 remainder 1Read the remainders from the bottom up: 19311111111 (base 2) = 193 (base 12)
Worked example 3: 1111101000 from binary to duodecimal
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 121,000 ÷ 12 = 83 remainder 483 ÷ 12 = 6 remainder 11 (B)6 ÷ 12 = 0 remainder 6Read the remainders from the bottom up: 6B41111101000 (base 2) = 6B4 (base 12)
Need the other direction? Open the Duodecimal to Binary converter.
Binary to Duodecimal examples
The decimal number 255 is written 11111111 in binary and 193 in duodecimal.
| Binary | Duodecimal | Decimal |
|---|---|---|
| 1 | 1 | 1 |
| 10 | 2 | 2 |
| 111 | 7 | 7 |
| 1000 | 8 | 8 |
| 1010 | A | 10 |
| 1111 | 13 | 15 |
| 10000 | 14 | 16 |
| 100000 | 28 | 32 |
| 1000000 | 54 | 64 |
| 1100100 | 84 | 100 |
| 11111111 | 193 | 255 |
| 1111101000 | 6B4 | 1000 |
Where Binary to Duodecimal 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.
Duodecimal (base 12) uses 0 to 9 plus A for ten and B for eleven. Twelve divides evenly by 2, 3, 4 and 6. That is why dozens, the 12-hour clock, twelve inches to a foot and twelve months feel natural. A few mathematicians even argue it is a better base than ten.
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 3 in duodecimal.
Binary to Duodecimal FAQ
How do I convert binary to duodecimal?
Convert to decimal first by adding up each digit times its place value, then divide that decimal number by 12 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 duodecimal number be longer or shorter?
Shorter. Going to a larger base packs more value into each digit, so the result is shorter. Roughly 0.28 duodecimal digits for every binary digit. The number 255 needs 8 digits in binary and 3 in duodecimal.
What is 11111111 in duodecimal?
11111111 in binary is 193 in duodecimal. 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.