Balanced Ternary Calculator
Convert and compute with digits T (−1), 0, and 1—no separate sign bit.
Balanced Ternary Calculator
Convert between decimal and balanced ternary using digits -1, 0, +1
Balanced Ternary Converter
Convert between decimal and balanced ternary (using -1, 0, +1)
Step-by-Step Conversion
About Balanced Ternary
- Balanced ternary uses digits -1, 0, and +1 (represented as T, 0, 1)
- No separate sign bit is needed - negative numbers are represented naturally
- Each position represents a power of 3, like regular ternary
- Used in the Soviet Setun computer, demonstrating practical ternary computing
- Offers advantages in arithmetic operations and circuit design
What balanced ternary is
Digits are T (−1), 0, and 1. Positions are powers of 3 (1, 3, 9, 27, …). Negatives come from T digits, so you do not need a leading sign the way two's complement does.
The Soviet Setun machines (Moscow State University, late 1950s–1960s) ran ternary hardware in practice. Binary won for industry; the number system is still a clean teaching example of a symmetric base.
Conversion examples
Decimal 11 → balanced ternary
Remainder 2 becomes T with carry +1 → result 11T
Check: 1×9 + 1×3 + (−1)×1 = 11
1T0T → decimal
1×27 + (−1)×9 + 0×3 + (−1)×1 = 17
Why people care
- Negation is digit flip (1↔T, 0 stays)—cheap conceptually
- Rounding to nearest integer is natural in this base
- Useful for teaching positional systems beyond binary/decimal
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Frequently Asked Questions
T vs −1?
Same value. T is the usual glyph so strings stay one character wide.
Vs ordinary ternary (0,1,2)?
Ordinary ternary needs a sign for negatives. Balanced ternary encodes sign in the digits.
How do I convert by hand?
Repeatedly divide by 3. Remainder 2 is written as T and you carry +1 into the next quotient. Read remainders from last to first.
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