Base 3 Computing Beats Binary

Original Article ↗ Hacker News Discussion ↗

Mathematical optimal base vs. real hardware

  • Several comments re-derive the “optimal radix” result: minimizing base × digits leads to base = e using calculus; among integers, 3 is closest to e.
  • Related reformulation: minimizing x / log x over x > 1 gives minimum at x = e; base-3 is the best integer.
  • Some note that this “radix economy” is a toy cost function and ignores hardware realities.

Physical / engineering constraints of ternary

  • Major theme: ternary gains in information density (~1.58 bits per trit) are modest and often outweighed by:
    • Harder discrimination between 3 voltage/charge levels.
    • Greater susceptibility to noise and tighter tolerances.
    • Likely need for higher supply voltages and more power dissipation.
    • Increased implementation complexity for gates and adders.
  • Disagreement over whether ternary must use negative voltages; some argue three positive levels suffice, others stress that intermediate levels are still problematic.
  • Multiple comments emphasize that binary CMOS has been optimized for decades; designing fast, low-power multi-level logic at GHz is a different and harder problem.

Existing multilevel and “ternary-like” technologies

  • NAND flash already stores multiple bits per cell via multiple charge levels (SLC/MLC/TLC/QLC), but this is used only for storage, with binary interfaces and substantial analog and ECC overhead.
  • High-speed links (Ethernet PAM-5, PCIe PAM-4, USB PAM-3, high-order QAM) use multi-level signaling for bandwidth, but internal computation remains binary.
  • Tristate / Hi-Z buses and open-collector/collector systems are discussed as three-state at the electrical level but still fundamentally binary in logic.

History and myths about ternary computing

  • The Soviet Setun machine is cited as a real ternary computer, though one comment notes it encoded trits using binary pairs.
  • Claims that the USSR “bet on ternary and lost the space race” are widely dismissed as fabrication or exaggeration.

Programming, logic, and architecture issues

  • Ternary control flow would naturally have three-way branches; some see this as occasionally useful (e.g., < / = / >, true / false / error), but others think most real branches are still binary (e.g., loop exits).
  • Some speculate about richer “tritwise” operations and ternary-native data types, but concrete killer examples beyond density are not provided.
  • Discussion of minimal ternary gate sets and balanced ternary arithmetic shows theoretical richness but also practical complexity.

Critiques of the article and overall sentiment

  • Many readers view the article as overselling ternary, leaning on simplistic arguments like “more than yes/no.”
  • Core consensus: mathematically, ternary (and e) is elegant; practically, binary remains superior given current device physics, tooling, and cost models. Enthusiasm is mostly theoretical; skepticism dominates on engineering grounds.