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The Abacus
© Copyright 1998, Jim Loy
On the left,
you see two abacuses (abaci is also correct). On both abacuses, we see the
number 1998. The top area of each abacus is used for fives, and the bottom area
is used for ones. Abacuses are used for doing arithmetic. When doing
arithmetic, you move the beads. The position of the beads represents the sum,
or product, so far. It is how you can remember the partial sum or product.
Experts in the use of the abacus can be very fast (and accurate), often faster
than an expert with a calculator, especially addition and subtraction. Such an
expert on the abacus is especially adept at data entry.
In the original version of this article, I mistakenly had the top area of
the two abacuses upside down. To start out, the abacus registers zero, with the
bottom (ones) beads all the way down, and the top (fives) beads up.
I won't get deeply into the mechanics of using an abacus. Let me just say,
to add one to a number, you either move a bead (in the rightmost
"ones" column) up, or move all four beads down then execute a carry
into the "fives" area. This carry just involves moving the five bead
down (remember that up is a zero and down is a five), or moving it up (to zero)
then executing a second carry into the "tens" column.
The Japanese abacus, the soroban, is more elegant, as the Chinese abacus
has redundant beads. With the Chinese abacus, you never have to use the bottom
bead in each column, in both the "ones" and "fives" areas.
These extra beads are apparently useful, if you use an extra step every time
you carry. You notice that you have all five beads up, so then you know you
should execute a carry.
Note: My dictionary shows an abacus with five beads below, but only
one bead above, a kind of combination of the two abacuses that I drew. And it
calls this a Japanese abacus. Apparently older Japanese abacuses were like
that. But, modern Japanese abacuses look much like the one that I show.
As I mentioned in one of my articles on Roman Numerals, the Soroban is
ideal for doing arithmetic with Roman Numerals. You just have to do a little
conversion, when spelling out the answers that contain IV, or IX, or XL, etc.
Here are some links to other abacus pages:
Just for fun, here is my binary (base 2) abacus, showing the number
1998.
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