Convert Binary to Ternary
Binary (base 2) to Ternary (base 3) number conversion — enter any value below to get an instant result, or use the table for common values.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
Result
"255" is not a valid Binary number — it contains a digit that base 2 doesn't support.
Conversion table: Binary to Ternary
| Decimal | Binary | Ternary |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 10 | 2 |
| 5 | 101 | 12 |
| 8 | 1000 | 22 |
| 10 | 1010 | 101 |
| 16 | 10000 | 121 |
| 32 | 100000 | 1012 |
| 64 | 1000000 | 2101 |
| 100 | 1100100 | 10201 |
| 255 | 11111111 | 100110 |
| 1000 | 1111101000 | 1101001 |
| 4096 | 1000000000000 | 12121201 |
| 65535 | 1111111111111111 | 10022220020 |
Binary (base 2)
Definition: Base 2 — every number is written using only the digits 0 and 1, where each position represents a power of two.
History: Formalized by Gottfried Wilhelm Leibniz in 1703, though similar two-symbol counting systems appear in ancient Chinese I Ching hexagrams. It became foundational to computing in the 1930s-40s once engineers realized electronic switches naturally represent two states: on and off.
Current use: The native language of digital computers — every value a computer stores, from a single character to an entire video file, is ultimately binary at the hardware level.
Ternary (base 3)
Definition: Base 3 — every number is written using the digits 0, 1, and 2, where each position represents a power of three.
History: Explored theoretically since the 18th century, ternary saw a rare practical implementation in the Soviet Setun computer (1958), which used "balanced ternary" (-1, 0, 1) because it was mathematically more efficient than binary for certain arithmetic.
Current use: Mostly a mathematical curiosity today, though balanced ternary occasionally resurfaces in computer science research and puzzles like the classic three-weight balance-scale problem.
Supported Number Systems
| System | Base | Digits used |
|---|---|---|
| Binary | 2 | 0-1 |
| Ternary | 3 | 0-2 |
| Octal | 8 | 0-7 |
| Decimal | 10 | 0-9 |
| Duodecimal | 12 | 0-B |
| Hexadecimal | 16 | 0-F |
| Base 32 | 32 | 0-V |
| Base 36 | 36 | 0-Z |
About These Parameters
- Value
- The number you want to convert, written using the "From" base's digits. Use letters A-Z for digit values 10 and above.
- From Base
- The numeral system your input value is currently written in.
- To Base
- The numeral system you want the result converted into. Use the swap button to flip From and To instantly.
How Number Base Conversion Works
The Formula
Every positional numeral system builds a value the same way: each digit is multiplied by the base raised to its position (counting from 0 on the right), and the results are summed.
value = d(n)×base^n + ... + d(1)×base^1 + d(0)×base^0
Why Hexadecimal Is Computing's Favorite Shorthand
Each hexadecimal digit represents exactly 4 binary bits (a "nibble"), so any binary string can be grouped into 4-bit chunks and converted to hex digit-by-digit, with no multiplication needed. Octal works the same way with 3-bit groups. This is why hex and octal became standard shorthand for binary data long before general-purpose calculators made arbitrary-base conversion easy.
Letters as Digits
Once a base exceeds 10, there aren't enough numerals to represent every digit, so letters fill the gap: hexadecimal uses A-F for the values 10-15, and base 36 uses the entire alphabet A-Z for the values 10-35 — the largest base that can be written with only the standard Latin letters and Arabic numerals.
Frequently Asked Questions
Why do computers use binary instead of decimal?
Digital circuits are built from switches that are most reliably built to have exactly two stable states (on/off, high/low voltage), which maps naturally onto the two binary digits, 0 and 1 — a 10-state decimal circuit would be far more complex and error-prone to build.
What does hexadecimal "FF" equal in decimal?
255 — F is 15 in each of the two digit positions, so it's 15×16¹ + 15×16&sup0; = 240 + 15 = 255, which is also why 255 is the maximum value a single 8-bit byte can hold.
Are these conversions exact for very large numbers?
Yes — this converter uses arbitrary-precision integer arithmetic internally rather than a fixed-size number type, so extremely long binary or base-36 values convert exactly with no overflow or rounding error.