How Base 3 Computing Beats Binary

Metadata

• Author: Stephen Ornes
• Category: rss
• URL: https://www.quantamagazine.org/how-base-3-computing-beats-binary-20240809/

Highlights

Three, as Schoolhouse Rock! told children of the 1970s, is a magic number. Three little pigs; three beds, bowls and bears for Goldilocks; three Star Wars trilogies. You need at least three legs for a stool to stand on its own, and at least three points to define a triangle.

If a three-state system is so efficient, you might imagine that a four-state or five-state system would be even more so. But the more digits you require, the more space you’ll need. It turns out that ternary is the most economical of all possible integer bases for representing big numbers.

Surprisingly, if you allow a base to be any real number, and not just an integer, then the most efficient computational base is the irrational number e.

Despite its natural advantages, base 3 computing never took off, even though many mathematicians marveled at its efficiency. In 1840, an English printer, inventor, banker and self-taught mathematician named Thomas Fowler invented a ternary computing machine to calculate weighted values of taxes and interest. “After that, very little was done for years,” said Bertrand Cambou, an applied physicist at Northern Arizona University.

Why didn’t ternary computing catch on? The primary reason was convention. Even though Soviet scientists were building ternary devices, the rest of the world focused on developing hardware and software based on switching circuits — the foundation of binary computing. Binary was easier to implement.