Page 77 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

58 Chaptersewen

years ago, our fathers brought forth upon this continent a new nation. . .” This all
serves to illustrate that number systems with bases other than ten are not only
possible, but positively abound throughout history.

Quinary (Base Five)
One system that is relatively easy to understand is quinary (base-5), which
uses the digits 0, 1, 2,3 and 4. This system is particularly interesting in that a
quinary finger-counting scheme is still in use today by merchants in the Indian
state of Maharashtra near Bombay.
As with any place-value system, each column in a quinary number has a
weight associated with it, where the weights are derived from the base. Each
digit is combined with its column’s weight to determine the final value of the
number (Figure 7 - 10).

Twenty-fives column
Fives column
Ones column

Figure 7-10. Combining digits with column weights in quinary

When using systems with bases other than ten, subscripts are used to indicate
the relevant base; for example, 3234, = 44410 (3234QUI~ARY = 444DEcImL).
By convention, any value without a subscript is assumed to be in decimal.
Counting in quinary commences at 0 and progresses up to 4,, at which
point all the available digits have been used. Thus, the next count causes the
first column to be reset to 0 and the second column to be incremented resulting
in lo,. Similarly, when the count reaches 4q5, the next count causes the first
column to be reset to zero and the second column to be incremented. But, as
the second column already contains a 4, this causes it to be reset to 0 and the
third column to be incremented resulting in 100, (Figure 7-1 1).