Math in Computing

Early Counting and Calculating Devices

How are modern abaci used?

Today’s standard abacus is typically constructed of wood or plastic and varies in size. Most are about the size of a small laptop computer. The frame of the device has a series of vertical rods or wires on which a number of wooden beads slide freely. A horizontal beam separates the frame into two sections called the lower and upper decks.

For example, in a Chinese abacus, the lower and upper decks each have 13 columns; the lower deck has five beads per column, while the upper deck has two beads. Each bead on the upper deck has a value of five, while each bead on the lower deck has a value of one (thus, it is called a 1/5 abacus). To use the abacus, users place the abacus flat on a table or their laps; they then push all the beads on the upper and lower decks away from the horizontal beam. From there, the beads are manipulated, usually with the index finger or thumb of one hand, to calculate a problem. For example, if you wanted to express the number 7, you would move two beads in the lower deck and one bead in the upper deck: (1 + 1) + 5 = 7.

This modern abacus is still used by shopkeepers in Asia and many so-called “Chinatowns” in North America. Students continue to be taught how to use the abacus in Asian schools, especially to teach children simple mathematics and multiplication. In fact, it is an excellent way to remember multiplication tables and is useful for teaching other base numbering systems, because it can adapt itself to any base. (For more about base numbers, see “History of Mathematics” and “Math Basics.”)


The beads are arranged in this illustration of an abacus to represent the number 38,704.


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