Understanding Base-2 vs. Base-10 Numeric Systems

The modern binary number system (base-2) dates back to an article by Gottfried Leibniz in 1679. Leibniz was able to interpret Chinese hexagrams as evidence of binary calculus. Binary systems are still used today, and that numeric system is exposed to average consumers every day, even though they probably don’t understand the system or why it is used with computer-related hardware and software.

In this article by Bruce Dawson, he asks the question of why we should expose the base-2 numeric system to the average computer user.

It’s 2016 and Windows still displays drive and file sizes using base-2 size prefixes. My 1 TB SSD is shown as 916 GB, and a 449 million byte video file is shown as 428 MB. That is, Windows still insists that “MB” means 2^20 and “GB” means 2^30, even when dealing with non-technical customers.

  1. This makes no sense.
  2. Just because some parts of computers are base 2 doesn’t mean all parts are base 2.
  3. And, actually, most of the visible parts of computers are base-10.

So just stop it. Base 2 prefixes should only be used when there is a compelling advantage for the typical user, and for file and drive sizes in Windows explorer there are no such advantages. If you think I’m wrong (and I know that lots of people do) then be sure to explain exactly why base-2 size prefixes make sense in the context of file and drive sizes.

You might also find it useful trivia that the ancient Sumerians (circa 3100 B.C.) used a base-60 numbering system, which we still use today for time and latitude measurements. A number of factors distinguishes the base-60 system from its base-10 counterpart, which likely developed from people counting on both hands. The base-60 system uses integers 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, while base-10 uses 1, 2, 5, and 10.

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