Balanced ternary is a non-standard positional system where each digit can be −1, 0, or +1. Instead of using the digits 0, 1, 2 as in standard ternary, it uses special symbols:
⊖ (U+2296, Circled Minus) represents −1, and ⊕ (U+2295, Circled Plus) represents +1.
Each position represents a power of 3, but digits can be negative:
For negative numbers, the signs of all non-zero digits are flipped (⊕ ↔ ⊖).
Balanced ternary has the unique property that the sign of a number can be determined from its most significant non-zero digit, eliminating the need for a separate sign. The system was studied by Leonardo Pisano (Fibonacci, 1170–1250) in connection with the weight problem — using weights of powers of 3, any integer mass from 1 can be measured with the fewest weights. In 1958, the Soviet engineer Nikolai Brusentsov built the Setun computer at Moscow State University, which used balanced ternary arithmetic and became one of the most elegant early ternary computers.