Ternary computing, also known as base 3 computing, is gaining attention for its remarkable efficiency compared to traditional binary systems. In a binary system, two bits can represent four numbers, while two trits in a ternary system can represent nine numbers. This efficiency means that a number requiring 42 bits in binary would only need 27 trits in ternary.
While one might think that systems with more states would be even more efficient, ternary systems are actually the most economical for representing large numbers. This is evident when considering the radix economy, which calculates the space needed to store data based on the base of the number system and the number of digits required. For example, representing the number 100,000 in base 10 requires 6 digits, resulting in a radix economy of 60. In binary, the same number requires 17 digits, with a radix economy of 34, while in base 3, it requires 11 digits with a radix economy of 33. Base 3 has the lowest radix economy for large numbers among all integer bases.
In addition to its numerical efficiency, base 3 computing offers computational advantages. In a binary system, queries can only have two possible answers, while ternary logic allows for three possible answers. This means that comparing two numbers in a ternary system only requires one query, simplifying the computational process.
Despite its efficiency, ternary computing did not gain widespread adoption due to convention and the focus on binary systems in the digital age. However, recent years have seen progress in developing ternary logical systems even on binary-based hardware. Engineers have proposed innovative ways to implement ternary computing, and researchers like Bertrand Cambou have been exploring cybersecurity systems based on base 3 computing. Cambou’s work has shown that using trits instead of bits can significantly reduce error rates in cybersecurity systems.
While ternary computing may not have taken off historically, it is now being reconsidered for its potential advantages in modern computing systems. As the world continues to explore new technologies and computing paradigms, the efficiency and computational advantages of base 3 computing are gaining recognition. Perhaps the future of computing truly lies in the magic number three.
