Page 75 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

56 w ChuprerSeven

convey certain advantages. Sixty is the smallest number that can be wholly
divided by 2 through 6; in fact, sixty can be wholly divided by 2,3,4,5, 6, 10,
12, 15, 20 and 30. Just to increase their fun, in addition to using base sixty the
Babylonians also made use of six and ten as sub-bases.

The Concepts of Zero and Negative Numbers
The concept of numbers like 1,2, and 3 developed a long time before the
concept of zero. In the original Babylonian system a zero was simply represented
by a space; the decimal equivalent would be as shown in Figure 7-8.
I
“126904” would be written a5 “1269 4”
“102056 would be written a5 “1 2 56”
“160014” would be written a5 “16 14”

Figure 7-8. Representing zeros using spaces

It is easy to see how this can lead to a certain amount of confusion,
especially when attempting to portray multiple zeros next to each other.
The problems can only be exacerbated if one is using a sexagesimal system
and writing on tablets of damp clay in a thunderstorm.
After more than 1500 years of potentially inaccurate calculations, the
Babylonians finally began to use a
The water clock, or Clepsydra, is an special sign for zero, which first ap-
ancient instrumen peared around 300 BC. Some say that
time which is believed to have
originated in Egy this was one of the most significant
inventions in the history of math-
mnctctnri nF I en
w. u hW...U...F. - .... ” a,..”..
hole through which the water ematics. However, the Babylonians
escaped. Units of time were only used the zero symbol as a place
on the side of the container or holder to separate digits- they didn’t
the ride of a bowl used to cnlle have the concept of zero as an actual
ater. The length of the un value. If we were to use the ‘A’ charac-
orresponding to day and
ould be adjusted by varyin ter to represent the Babylonian place
he shape of the container; holder, the decimal equivalent to the
. . . . _. clay tablet accounting records of the
-
time would read something like that
shown in Figure 7-9.