The evolution of number systems has been a fascinating journey through human history. From the Babylonians’ intricate combinations of symbols to our modern decimal system, numbers have been represented in various ways over time. But what about computers? How do they process information, and is there a better number system for them than the binary system we currently use?
Computers, with their binary system of 0s and 1s, are incredibly efficient at processing information. However, in the past, experts explored the idea of ternary systems, which use three digits (0, 1, and 2) to represent numbers. The hope was that a ternary system would allow for more efficient information processing. But why did ternary computers not take off, and why is the binary system still prevalent today?
In theory, any number can be represented in any number system, whether it be base 10, base 60, base 3, or base 2. The math works perfectly in each case. However, when it comes to practicality, the binary system has a clear advantage over other systems, including ternary.
For example, let’s look at how the number 17 is represented in different number systems. In base 10 (decimal), 17 is written as 17 = 1 Ă— 10 + 7 Ă— 1. In base 3 (ternary), 17 is written as 1710 = 1 Ă— 32 + 2 Ă— 31 + 2 Ă— 30 = 1223. And in binary, 17 is written as 1710 = 1 Ă— 24 + 0 Ă— 23 + 0 Ă— 22 + 0 Ă— 21 + 1 Ă— 20 = 10,0012.
Comparing these representations, the decimal system is the most efficient, requiring only two digits to represent 17. However, the binary system, while less efficient in terms of digits needed, is better suited for practical implementation in computers. In conventional computers, the hardware is designed to interpret 0s and 1s, making the binary system the most practical choice.
But what about the idea of a more balanced ternary system, where numbers are represented using 0, 1, and 2, or even -1, 0, and 1? The balanced ternary system offers symmetry and unique properties that have intrigued mathematicians and computer scientists.
In the balanced ternary system, the number 17 is represented as 1710 = 1 Ă— 33 + (–1) Ă— 32 + 0 Ă— 31 + (–1) Ă— 30 = 1(–1)0(–1). This system has been described as “the prettiest number system of all” by computer scientist Donald E. Knuth.
In the 1840s, English inventor Thomas Fowler built a calculating machine that operated using the balanced ternary system. This mechanical computer used the numbers -1, 0, and 1 to perform calculations, offering a different logic than today’s computers. The ternary system’s unique properties allowed for shortcuts in certain calculations, making it an intriguing alternative to the binary system.
While the binary system remains the standard for computers today, the exploration of ternary systems continues to inspire new ideas and innovations in the field of information processing. Who knows what the future may hold for number systems and their impact on technology. A Ternary Computer: A Unique Innovation from the Cold War Era
In the world of computing, binary systems have long been the standard. However, there was a time when ternary computers, capable of counting in threes, were also in existence. One such example is the Setun, the first electronic ternary computer developed behind the Iron Curtain in the Soviet Union during the early years of the cold war.
In 1958, Moscow State University unveiled the Setun, a groundbreaking electronic computer that operated using ternary digits, or “trits.” Unlike conventional binary computers that rely on transistors, the Setun utilized magnetic cores and diodes for its processing capabilities. Despite its innovative design, only around 50 Setun computers were ever produced.
The main challenge with ternary computers, as opposed to binary systems, lies in the hardware and coding conventions. It is inherently more complex to design electronic components that can effectively represent three different states. In the case of the Setun, researchers had to use two magnetic components per trit, whereas in a binary system, the same components could encode twice as many bits.
Today, all modern computers operate on binary systems, utilizing transistors that can either allow current to flow (1) or not (0) through their inputs and outputs. By cleverly arranging these transistors into logic gates, computers can perform a wide range of calculations and operations efficiently.
While hobbyists have dabbled in developing ternary computers for fun, the fundamental differences between ternary and binary systems make it impossible to integrate the two. Despite this limitation, the unique capabilities of a ternary computer, even if comparable to conventional devices, highlight the fascinating diversity in computing technologies.
In conclusion, the legacy of the Setun serves as a reminder of the innovative spirit that drove computer development during the cold war era. While ternary computers may not have gained widespread adoption, their brief existence offers a glimpse into the diverse possibilities that exist within the realm of computing technologies.
This article was originally published in Spektrum der Wissenschaft and has been repurposed with permission.
