the idea
Why balanced ternary?
Three states per digit instead of two, with zero in the middle: −1, 0, +1. It is not a curiosity — it was built, it shipped, and its arithmetic is quietly more elegant than the binary we all learned.
It was a real machine
Setun — named after the river near Moscow State University — was designed there by Nikolay Brusentsov and runs in the computational center's memory of 1958. About fifty machines were built and used for over a decade: real programs, real engineering problems, real decimal input converted to balanced ternary in hardware. Its word was eighteen trits — three of this site's six-trit words. A successor, Setun-70, followed in 1970.
The machine here is deliberately small — six trits, one word, 729 values — so the whole architecture fits on a page. But everything it does is what Setun's arithmetic did. The word lab can widen it to eighteen and the same ring laws hold.
Three choices beat two
A bit can answer two questions; a trit can answer three. Every digit triples the values a word can hold instead of doubling them — so a ternary word packs about 1.58× more value per digit than a binary one.
digits vs values
The sign lives inside the digits
Binary wastes a column on signs — a bit that says "negative" and a two's-complement rule to remember. Balanced ternary needs none of it: a digit is −1, 0, or +1, so negativity is just which way the most significant trit leans. Negation is flipping every trit, and nothing is ever "unsignable."
word dial
Watch the dial: set the −1 column and the value obeys. There is no separate sign — - is not a flag, it is a digit.
Balanced rounding is exact, on average
Division rounds to the nearest representable value, with ties away from zero. Binary rounding drifts toward one side because its digit set is lopsided (0 and 1); balanced ternary's set is centered, so rounding errors cancel instead of accumulating. That property made Setun's fixed-point arithmetic famous for staying honest.
Arithmetic wraps instead of lying
When a result leaves the ring, the machine wraps it around and sets the overflow flag — loudly, visibly, on +- rings like the number converter's ring. The wrap is not a bug to hide: it is the machine telling you the number grew past its word, in the same balanced digits everything else uses.
try it
Open the labs and pass "The 4-trit machine" — 10 × 10 becomes 19, and you will see why.