Eleventy What?

TheFr00n asks: "I recently managed to teach my ten year old son the hexadecimal number system, but he shot me back a question that has me stumped. How does one pronounce hex, after the first iteration? In decimal, we have nice words like 'fifty' and 'sixteen'. Is there an official way of pronouncing a hexadecimal number like CF9? 'See hundred and effty-nine'? (which is totally wrong anyway because a hundred is 64 in hexidecimal) Any thoughts?"

As a programmer 20 some years ago...

[DaoudaW]

Finally something I know something about. "One, two, three, four, five, six, seven, eight, nine, able, baker, Charlie, dog, easy, fox, one-zero. One-one, one-two, one-three, one-four, one-five, one-six, one-seven, one-eight, one-nine, one-able, one-baker, one-Charlie, one-dog, one-easy, one-fox, two-zero. Two-one, two-two, two-three..." Three digit numbers likewise: "One-zero-nine, one-zero-able, one-zero-baker,..., nine-fox-fox, able-zero-zero."

Re:As a programmer 20 some years ago...

[DaoudaW]

I've done that one when operating an aviation radio, but for hexadecimal I've only ever heard "able, baker, charlie, dog, easy, fox".

dek el zen tris cat kink

[PurpleBob]

Well, I don't know how to solve the problem of "hundred". But the digits can have names (and not just the letter names, which have the problem that they're hard to tell apart and A sounds like 8).

On Everything2, there's the node Names for digits higher than 9 [everything2.com]. The names for the digits - I have no idea who created them - are "dek" for A, "el" for B, "zen" for C, "tris" for D, "cat" for E, and "kink" for F.

Donald Knuth Has The Answer

[Sunlighter]

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.

Re:Donald Knuth Has The Answer

[nickos]

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.