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Balanced ternary is a ternary numeral system (i.e. base 3 with three digits) that uses a balanced signed-digit representation of the integers in which the digits have the values −1, 0, and 1. This stands in contrast to the standard (unbalanced) ternary system, in which digits have values 0, 1 and 2. The balanced ternary system can represent all integers without using a separate minus sign; the value of the leading non-zero digit of a number has the sign of the number itself. The balanced ternary system is an example of a non-standard positional numeral system. It was used in some early computers and also in some solutions of balance puzzles.

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  • Balancovaná trojková soustava (cs)
  • Balanced ternary (en)
  • Sistema numerico ternario bilanciato (it)
  • 균형 3진법 (ko)
  • System trójkowy zrównoważony (pl)
  • Ternário balanceado (pt)
  • 平衡三進位 (zh)
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  • Balancovaná trojková soustava nebo též balancovaná ternární soustava je speciální poziční číselná soustava, používající znaky s významy 0, 1 a -1. Tím se liší od „normální“ ternární soustavy, obsahující znaky 0, 1 a 2. Soustava - stejně jako jiné balancované číselné soustavy - umožňuje přímý zápis záporných čísel. Byla použita u některých experimentálních třístavových počítačů (např. sovětský a ). (cs)
  • Il ternario bilanciato è un sistema numerico posizionale non standard. È un sistema in base 3, che, a differenza del sistema ternario standard, usa come cifre -1, 0 e 1 anziché 0, 1 e 2. Le potenze di 3 usate per rappresentare il numero possono avere quindi coefficiente positivo, nullo o negativo. La seguente tabella elenca i primi 12 numeri scritti nel sistema decimale, ternario e ternario bilanciato (viene usato il simbolo 1 per rappresentare la cifra -1). (it)
  • 균형 3진법은 밑이 3이고 자릿수가 -1,0,1인 비표준 위치 기수법이다. 한자리 수의 곱셈이 한자리 수가 되고, 부호 전환이 간단하다는 특징을 가진다. 이러한 특징으로 인해 3진법 컴퓨터의 주된 기수법으로 쓰인다. 대표적으로 세르게이 리보비치 소볼레프의 세툰이 균형 3진법을 사용했다. (ko)
  • System trójkowy zrównoważony – pozycyjny system liczbowy o podstawie 3 używający cyfr: −1, 0, 1. Zwykłe systemy pozycyjne używają cyfr od zera do cyfry o jeden mniejszej niż podstawa systemu. Np. system dziesiętny stosuje cyfry 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. System trójkowy zrównoważony stosuje cyfry −1, 0, 1, dzięki czemu do zapisu liczby ujemnej nie jest potrzebny znak „minus”. Zamiast cyfr 1 i −1 zwykle stosuje się znaki + i −. Liczba 100 zapisuje się jako 81+27−9+1, czyli 34+33−32+30, co daje nam ciąg ++−0+ (zero symbolizuje nieistniejący składnik 31). (pl)
  • 平衡三进制（英語：balanced ternary）是一種非標準的計數进位制，它是一種基數為的进位制系統，其中用於計數的符码為，與標準基數 3 进制系統對比：其中的計數符號為。以平衡三进制所記錄的數字可以表達出全部整數，由于的引入，而且對负数不必使用额外的负號；應用在於解決秤重問題，或在一些早期的計算機中使用。 有些地方使用不同符码來表示平衡三进制中的三個數符。本文中以 T（連在 1 上方的负號）表示 ，而 和 表示自身。其他約定包括使用 '-' 和 '+'分別表示 和 ，或使用希臘字母 Θ（於圓圈中的负號）來表示 。在 Setun計算機中 表示為倒轉的阿拉伯數字一：「1」。 平衡三进制在 Michael Stifel（1544）的書《Arithmetica Integra》中出現過。它也曾出現在 Kepler和 LéonLalanne 的作品中。對负数不必使用额外的负號这一点，使得平衡三进制在四则运算的加、減、乘法效率，會比二进制高。美国著名计算机学家高德纳在《编程的艺术》一书中指出，“也许最美的进制是平衡三进制”。 (zh)
  • Balanced ternary is a ternary numeral system (i.e. base 3 with three digits) that uses a balanced signed-digit representation of the integers in which the digits have the values −1, 0, and 1. This stands in contrast to the standard (unbalanced) ternary system, in which digits have values 0, 1 and 2. The balanced ternary system can represent all integers without using a separate minus sign; the value of the leading non-zero digit of a number has the sign of the number itself. The balanced ternary system is an example of a non-standard positional numeral system. It was used in some early computers and also in some solutions of balance puzzles. (en)
  • Ternário balanceado é um sistema numeral posicional não-padrão (uma ), útil para a lógica de comparação. É um sistema ternário, mas ao contrário do sistema ternário padrão (desequilibrado), os dígitos têm valores -1, 0 e 1. Essa combinação é especialmente valiosa para as relações ordinais entre dois valores, onde as três possíveis relações são menos-que, igual-a e maior-que. O ternário balanceado pode representar todos os inteiros, sem recorrer a um sinal de menos. (pt)
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