Beyond Binary: The Case for Ternary Computing

For over half a century, computing has been dominated by binary logic—ones and zeros, high and low voltage, on and off. This simple, resilient scheme matches the physical world well and has built the technological landscape we stand on today. Transistors, the most-produced artifact in human history, number in the sextillions, all operating on this foundation of two states.

But binary is not the only possibility. Ternary computing—based on three states instead of two—has long intrigued researchers. In ternary, a single digit (called a “trit” or trinary digit) can hold more information than a bit.

• Unbalanced ternary uses {0, 1, 2}.

• Balanced ternary uses {–1, 0, +1}.

This second form, balanced ternary, has special elegance:

• Arithmetic is simplified (negative numbers are natural, not an afterthought).

• Certain operations require fewer steps.

• Representations become more compact.

For example:

• Binary 1101 = 13 in decimal.

• Unbalanced ternary 111 = 13 in decimal.

• Balanced ternary 1T1 (numeric style, where T = -1) or (1)(-1)(1), written symbolically as +–+ = 13 in decimal.

Reading ternary means stacking powers of 3, just as binary stacks powers of 2. The base-3 expansions look unusual at first, but they unfold with remarkable efficiency. The table below illustrates how balanced ternary logic extends binary truth tables and arithmetic. The top row shows logical operations (NOT, AND, OR) applied to trits (-1, 0, +1). The lower row shows arithmetic rules for ternary multiplication and addition, including carry-over to the next trit. These tables were part of the design work for Setun, the Soviet ternary computer developed in 1956, which demonstrated the practical elegance of balanced ternary in real hardware.

Graziap89, CC BY 3.0 <https://creativecommons.org/licenses/by/3.0>, via Wikimedia Commons

So why didn’t ternary win? Momentum. By the time ternary systems were explored (notably in the Soviet computer), the binary transistor infrastructure was already scaling rapidly. Industry investment, manufacturing pipelines, and educational pathways cemented binary as the “one true path.” Additionally, ternary logic faced a practical hurdle: noise margins. In binary, distinguishing between two voltage levels (high and low) is relatively robust, even with electrical interference. But, ternary requires three distinct levels, which means two thresholds must be resolved cleanly. With mid-20th century technology, those boundaries were fragile—susceptible to noise, heat, and component imperfections. The elegance of balanced arithmetic was real, but the hardware to support it was simply to delicate for mass adoption.

Where does ternary fit today?

• Specialized hardware: logic compression, balanced arithmetic.

• Theoretical exploration: AI architectures and novel processor design.

• Inspiration for the leap beyond silicon: quantum computing.

Qubits, with their superposition of many states, overshadow trits as the “future of future computing.” Yet ternary remains a reminder: the digital world was never limited to ones and zeros—it was a choice that fit the time. And choices can change.

References:

• Anastasi in Tech, Why Binary Won (and Ternary Lost) [YouTube].

• Donald E. Knuth, The Art of Computer Programming, Volume 2 (balanced ternary discussion).

• Graziap89, CC BY 3.0 <https://creativecommons.org/licenses/by/3.0>, via Wikimedia Commons

• L. N. Korolev, Setun: A Ternary Computer (Soviet ternary experiments).