Binary to Base-3 Converter
Convert binary integers to base-3 (ternary) instantly. Enter a binary value such as 11001 to see its decimal value, ternary representation, repeated-division steps, and exact conversion result.
What Is Binary to Base-3 Conversion?
Binary to base-3 conversion changes a number written in base 2 into an
equivalent number written in base 3. Base 3 is also called the ternary numeral
system and uses the digits 0, 1, and 2.
How to Convert Binary to Base-3
1. Read the binary input
Start with the binary integer containing only 0 and 1.
2. Convert binary to decimal
Use powers of 2 to find the numerical value of the binary input.
3. Divide the decimal value by 3
Record the quotient and remainder.
4. Repeat division by 3
Continue dividing each quotient until it becomes zero.
5. Record each remainder
Each remainder will be 0, 1, or 2.
6. Read remainders backward
Reverse the remainder sequence to obtain the base-3 result.
Example: Convert Binary 1010 to Base-3
Example: Convert Binary 11001 to Base-3
Binary to Base-3 Conversion Table
| Binary | Decimal | Base-3 |
|---|---|---|
0 | 0 | 0 |
1 | 1 | 1 |
10 | 2 | 2 |
11 | 3 | 10 |
100 | 4 | 11 |
101 | 5 | 12 |
110 | 6 | 20 |
111 | 7 | 21 |
1000 | 8 | 22 |
1001 | 9 | 100 |
1010 | 10 | 101 |
11001 | 25 | 221 |
What Is Base 3?
Base 3 uses three symbols:
For example, base-3 221 means:
Binary vs Base-3
| Feature | Binary | Base-3 |
|---|---|---|
| Base | 2 | 3 |
| Allowed digits | 0, 1 | 0, 1, 2 |
| Place values | Powers of 2 | Powers of 3 |
| Decimal 10 | 1010 |
101 |
| Decimal 25 | 11001 |
221 |
Why Convert Through the Numeric Value?
Binary and ternary bases are not powers of one another, so there is no simple fixed-size bit grouping similar to binary-to-octal or binary-to-hex conversion.
The reliable method is to interpret the binary number’s exact numerical value and then express that same value using powers of 3.
Does Leading Binary Zero Matter?
No. Leading zeros do not change the numerical value.
Common Binary to Base-3 Mistakes
Using digit 2 in binary input
Binary inputs can contain only 0 and 1.
Grouping binary bits
Unlike octal or hexadecimal conversion, fixed-size grouping does not directly convert binary to base 3.
Reading remainders top to bottom
Repeated-division remainders must be read from the final remainder back to the first.
Using digit 3 in the result
A base-3 numeral can contain only digits 0, 1, and 2.
Related BinaryCon Tools
Binary to Base-3 Converter FAQs
How do you convert binary to base 3?
What is binary 10 in base 3?
10 equals decimal 2, so its base-3 representation is 2.
What is binary 101 in base 3?
101 equals decimal 5. Decimal 5 is base-3 12.
What is binary 1010 in base 3?
1010 equals decimal 10, which is base-3 101.
What is binary 11001 in base 3?
11001 equals decimal 25, which converts to base-3 221.
What digits are allowed in base 3?
0, 1, and 2.