Question

I’ve been reading hexadecimal on a digit by digit basis for many years and am now fed up with translating hex values for numbers requiring more than 16 bits into English. Does a more elegant form of translating hexadecimal to English exist?

In English, a simple system exists for converting decimal values to English. Decimal 10 is English “ten”, decimal 57 is english “fifty-seven”, decimal 32767 is “thirty-two thousand seven hundred sixty-seven”, etc.

As far as I know, there exists no system for elegantly representing hexadecimal in English. Hexadecimal 10 is English “one zero” or “one oh”, hexadecimal F0ED is “eff oh eee dee”, hexadecimal 30F538B9310 is English “three oh eff five three eight bee nine three one oh”. Values requiring more bits become increasingly painful to translate. Sometimes converting it to the decimal equivalent to get an elegant English translation, so hexadecimal 10 becomes “sixteen”.

Thanks for any help.

Answer 1

This is in Knuth – googling the phrase “vybong bysanton” (which has stuck in my mind ever since reading it) produces this slashdot comment and response:

In section 4.1 of The Art of Computer
Programming, Donald Knuth describes:

…a prominent Swedish-American civil engineer named John W. Nystrom
[who] decided to… [devise] a
complete system of numeration,
weights, and measures based on
radix-16 arithmetic. He wrote, “I am
not afraid, or do not hesitate, to
advocate a binary system of arithmetic
and metrology. I know I have nature on
my side; if I do not succeed to
impress upon you its utility and great
importance to mankind, it will reflect
that much less credit on our
generation, upon our scientific men
and philosophers.” Nystrom devised
special means for pronouncing
hexadecimal numbers; for example,
[0xC0160] was to be read “vybong,
bysanton.” His entire system was
called the Tonal System, and it is
described in J. Franklin Inst. 46
(1863), 263-275, 337,348, 402-407.

Maybe you should get that issue of
that journal and give it a try.

(response:)

quoted from http://www.monmouth.com/~colonel/tonal.html [monmouth.com]

From Recreations in Mathematics, by H. E. Licks (Van Nostrand, 1917):

John W. Nystrom of Philadelphia devised about fifty years ago the tonal system&quot of
numeration in which 16 is the base instead of 10 as in the decimal system. The numerals 1, 2, 3,
4, etc., were called An, De, Ti, Go, etc., and new characters were devised for 10, 11, 12, 13, 14,
15. This system embraced also a new division of the year into 16 months, these having the names
Anuary, Debrian, Timander, Gostus, Suvenary, Bylian, Ratamber, Mesidius, Nictorary, Kolumbian,
Husander, Victorius, Lamboary, Polian, Fylander, Tonborious, the first two letters of each month
being the names of the sixteen numerals.

This is slightly inaccurate. The figure 9 was used for 10, on the principle of making the digits
for 8 or greater look like those of their 16’s complements written upside down; and a new figure
was devised for 9. The name of 12 was Vy, not Vi; and I believe that the meth, nith, vyth, and
tonth months were named Mesudius, Nictoary, Vyctorius, and Tonborius.

The year began at the winter solstice, that being the Anth of Anuary. Every month had tonra days
except for Debrian, Gostus, and Lamboary, which had only tonby, but Debrian had an extra day in
leap years.

The powers of ton were: ton, san, mill, bong. These could be used as prefixes to indicate
multiplication or as suffixes to indicate division. For instance, the day was divided into ton
(sixteen) tims, a tim into ton timtons, and a timton into ton timsans.