Page 74 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Alternative Numbering Systems 55

If a similar finger-joint counting
strategy is applied to both hands,
the counter can represent values from
1 through 24 (Figure 7-6).
This may explain why the ancient
Egyptians divided their days into
twenty-four periods, twelve for day
and twelve for night. Once again, the
lengths of the periods were adjusted to
the seasons, but were approximately
equal to one of our hours.
Figure 7-6. Using finger joints on
Sexagesimal (Base-60) both hands to count to twenty-four
The ancient Babylonians used a sexagesimal (base-60) numbering system.
This system, which appeared between 1900 BC and 1800 BC, is also credited as
being the first known place-value number system. While there is no definite
proof as to the origins of the sexagesimal base, it’s possible that this was an
extension of the finger-joint counting schemes discussed above (Figure 7-7 >.
The finger joints of the left hand are still used to represent the values one
through twelve; however, instead of continuing
directly with the finger joints of the right hand, 5x12
the thumb and fingers on the right hand are used 4x12
3x12
to keep track of each count of 2x12
twelve. When all of the right I XI2
hand digits are extended the
count is sixty (5 x 12 = 60).

Although sixty may
appear to be a large value

to have as a base, it does

2 After reading this book, one of
the author’s friends found this
technique useful to keep track of
her child’s finishing position in a
cross-country run. Figure 7-7. Using fingers to count to sixty2