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November 5, 2016

Hexadecimal Numerals

I was recently asked what symbols I would add the sequence of numerals in order to provide a complete set for the hexadecimal (base 16) number system. My approach to this problem is to follow two principles:

  1. Go back to the same tradition that produced the Hindu-Arabic numerals in common use worldwide.
  2. Adopt symbols that are easily distinguished from the existing numerals 1 through 9 and that lend themselves to stylistic variation

Hindu-Arabic numerals in use today can be broadly categorized as the variants in use in various scripts of India, Arabic and the now commonly accepted “universal” numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). The origin of these latter numbers goes back to the Brahmi script of India. As with many concepts, these numbers made their way via the Islamic golden age of learning (c. 12th to 14th centuries CE) and into the European Renaissance, with the current form of the numbers known definitively in the 16th century etchings of Albrecht Dürer. I give the origin of the basic form of each numeral below. Note that all the scripts referenced evolved from Brahmi script.

Assuming that the new hexadecimal number system will be used consistent with itself, I propose to adapt already known numerals for 10, 1, 2, 3, 4 and 5. Ten will remain itself, while the other five numerals will be repurposed as 11, 12, 13, 14 and 15 in the new system. While it is true that these numerals will be similar to symbols already in use, it should be clear that they are being read in a new context and thus not cause confusion. I have elected not to use Greek letters as they are already in extensive use as mathematical symbols and hence are not available to be given these new numerical values.

The numerals have been adopted as follows:

10: Roman numeral X or the Chinese character for ten, which is a larger version of +
11: The numeral one as used in various styles in Lao, Thai and Kannada scripts
12: The numeral two from Laotian script
13: The numeral three from Malayalam script
14: The numeral four from Telegu script
15: The numeral five from Brahmi script