Page 76 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Alternative Numbering Systems 57

Qriginal Amount - Fish Distributed = Fish Remaining
1852 fish - 45 fish to 5teph = lAA7 fish
- 2A fish to Max = 987 fish
- 4A7 fish to Lucie = 588 fish
- 176 fish to Drew = 4A4 fish
- 4A4 fish to Abby = “No fish left”

Figure 7-9. Representing zeros using a place-holder
The last entry in the “Fish Remaining” column is particularly revealing.
Due to the fact that the Babylonian zero was only a place holder and not a
value, the accounting records had to say “No fish left” rather than “A fish. ’’
In fact, it was not until around 600 AD that the use of zero as an actual value
first appeared in India.

Vigesimal (Base-20)
The Mayans, Aztecs, and Celts developed vigesimal (base-20) systems by
counting using both fingers and toes. The Eskimos of Greenland, the Tamanas
of Venezuela, and the Ainu of northern Japan are three of the many other
groups of people who also make use of vigesimal systems. For example, to say
fifty-three, the Greenland Eskimos would use the expression “lnup pingu - j u sane
g
urkanek-pingcisut,” which translates as “Of the third man, three on the first f00t.l’~
This means that the first two men contribute twenty each (ten fingers and ten
toes), and the third man contributes thirteen (ten fingers and three toes).
To this day we bear the legacies of almost every number system our ancestors
experimented with. From the duo-decimal systems we have twenty-four hours
in a day (2 x 12), twelve inches in a foot, and special words such as dozen (12)

and gross (144). Similarly, the Chinese have twelve hours in a day and twenty-
four seasons in a year. From the sexagesimal systems we have sixty seconds in a
minute, sixty minutes in an hour, and 360 degrees in a ~ircle.~ From the base
twenty systems we have special words like score (20), as in “FQUT score and seven

3 George Ifrah: From One to Zero (A Universal History of Numbers) .
4 The 360 degrees is dlerived from the product of the Babylonian’s main base (sixty) 2nd their
sub-base (six); 6 x 60 = 360.