John W. Nystrom (Swedish: Johan Vilhelm Nyström) (1825-1885) was a Swedish-American civil engineer, inventor and author who lived in Philadelphia, Pennsylvania.
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He was born Johan Vilhelm Nyström in Småland province, Sweden.
Nystrom received many patents for inventions such as a marine steam engine, a refrigerator, and calculating machines. His slide ruler invention (U. S. patent #7961) was filed with the United States Patent Office on March 4, 1851.[1]
Nystrom is most noted for his proposal to switch from base 10 to base 16 as defined in his 1862 publication titled Project of a New System of Arithmetic, Weight, Measure and Coins, Proposed to be Called the Tonal System, with Sixteen to the Base.
In 1859, Nystrom proposed a hexadecimal (base 16) system of notation, arithmetic, and metrology called the Tonal System. In addition to new weights and measures, his proposal included a new calendar with sixteen months, a new system of coinage, and a hexadecimal clock with sixteen hours in a day.
"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 upon our generation, upon scientific men and philosophers."
(Quotation: John W. Nystrom, ca. 1863)[2]
He proposed names for the hexadecimal digits, calling zero "noll" and counting (from one to sixteen):
"An, de, ti, go, su, by, ra, me, ni, ko, hu, vy, la, po, fy, ton." (Therefore tonal system.)
Because hexadecimal requires sixteen digits, Nystrom supplemented the existing decimal digits 0 through 8 with his own invented characters. (These can be seen on his clockface at right.) Modern users of hexadecimal overcome this same obstacle by using the digits 0 through 9 followed by the letters A through F.
The numbers 1116 and 1216 would be said "tonan", "tonde", etc. The table below shows Nystrom's names for successive powers of 1016.
| Base 16 Number | Tonal Name | Base 10 Equivalent |
|---|---|---|
| 10 | ton | 16 |
| 100 | san | 256 |
| 1000 | mill | 4,096 |
| 1,0000 | bong | 65,536 |
| 10,0000 | tonbong | 1,048,576 |
| 100,0000 | sanbong | 16,777,216 |
| 1000,0000 | millbong | 268,435,456 |
| 1,0000,0000 | tam | 4,294,967,296 |
Thus, the hexadecimal number 1510,0000 would be "mill-susanton-bong". This first hexadecimal system, proposed in the 19th century, has thus far not achieved widespread usage.
By 1875, Nystrom had abandoned his Tonal System, and proposed a new proposed duodecimal (base 12) system of notation, arithmetic, and metrology called the Duodenal System as an appendix in his book "A New Treatise on Elements of Mechanics Establishing Strict Precision in the Meaning of Dynamical Terms".