Binary to Ternary Converter
Type a binary number to see it in ternary. Below: how the conversion works, a worked example and a conversion table.
11111111 binary = 100110 ternary
How to convert binary to ternary
Go through decimal: first multiply each digit by 2 raised to the power of its position (counting from 0 on the right) and add the results; then divide the number by 3 again and again and write down the remainders; read in reverse order, the remainders are the ternary digits.
Example: 11111111 to ternary
Step 1: Binary to decimal
Multiply each digit by 2 to the power of its position (0 on the right), then add:
| Digit | Place value | Digit × place |
|---|---|---|
1 | 27 = 128 | 128 |
1 | 26 = 64 | 64 |
1 | 25 = 32 | 32 |
1 | 24 = 16 | 16 |
1 | 23 = 8 | 8 |
1 | 22 = 4 | 4 |
1 | 21 = 2 | 2 |
1 | 20 = 1 | 1 |
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255
Step 2: Decimal to ternary
Divide by 3 repeatedly and keep the remainders. Reading the remainders from the last one to the first gives the ternary digits:
| Division | Quotient | Remainder (digit) |
|---|---|---|
| 255 ÷ 3 | 85 | 0 |
| 85 ÷ 3 | 28 | 1 |
| 28 ÷ 3 | 9 | 1 |
| 9 ÷ 3 | 3 | 0 |
| 3 ÷ 3 | 1 | 0 |
| 1 ÷ 3 | 0 | 1 |
Result: 255 = 100110 in ternary.
Binary to Ternary table
| Binary | Ternary |
|---|---|
0 |
0 |
1 |
1 |
10 |
2 |
11 |
10 |
100 |
11 |
101 |
12 |
110 |
20 |
111 |
21 |
1000 |
22 |
1001 |
100 |
1010 |
101 |
1011 |
102 |
1100 |
110 |
1101 |
111 |
1110 |
112 |
1111 |
120 |
10000 |
121 |
100000 |
1012 |
1000000 |
2101 |
1100100 |
10201 |
1111111 |
11201 |
10000000 |
11202 |
11111111 |
100110 |
100000000 |
100111 |
1000000000 |
200222 |
1111101000 |
1101001 |
1111111111 |
1101220 |
10000000000 |
1101221 |
Binary to other systems
Other systems to ternary
Reverse conversion
Frequently asked questions
How do you convert binary to ternary?
Go through decimal: first multiply each digit by 2 raised to the power of its position (counting from 0 on the right) and add the results; then divide the number by 3 again and again and write down the remainders; read in reverse order, the remainders are the ternary digits.
What is 11111111 in ternary?
11111111 in binary is 100110 in ternary.