Page 72 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Alternative Numbering Systems II 53
.1..
- Thousands column
Hundreds column
Tens column
Ones column

3234
+
= (3 1000) (2 x 100) + (3 10) + (4 1)
x
x
x
Figure 7-2. Combining digits with column weights in decimal

up to 9, at which point all of 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 10. Similarly, when the count reaches 99, 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 9, this causes
it to be reset to 0 and the third column to be incremented resulting in 100
(Figure 7-3).
Although base- 10 systems are anatomically convenient, they have few
other advantages to recommend them. In fact, depending on your point of
view, almost any other base (with the possible exception of nine) would be
as good as, or better than, base-10, which is only wholly divisible by 2 and 5.
FOR many arithmetic opera-
tions, the use of a base that is 1
1
wholly divisible by many V j,
numbers, especially the smaller 0 10 20 100
values, conveys certain advan- 1 11 21 101
tages. An educated layman may 2 12 22 102
well prefer a base-12 system on
the basis that 12 11s wholly
divisible by 2, 3, 4 and 6. For
their own esoteric purposes,
some mathematicians would 8 18 98 998
ideally prefer a system with a 9 19 99 999
prime number as a base; for I
example, seven oir eleven.
Figure 7-3. Counting in decimal