An early mechanical calculator whose design has evolved through the centuries, with two styles in use today. Both the Chinese and the Japanese styles consist of a frame with a crossbeam. They may be made from many different materials, such as wood or brass. Rods or wires carrying sliding beads extend vertically through the crossbeam. The Chinese suan pan has two beads above the beam on each rod and five beads below. Each rod of the Japanese soroban carries one bead above and four below. Similar to the abacus in both construction and use, but much larger, are the counting frames used in elementary schools. Braille versions of the abacus are available for use by those without sight.
In working with whole numbers, the rightmost rod represents the ones position, with each rod to the left representing the tens, hundreds, thousands, and so forth, respectively. The beads below the crossbeam represent one of that rod's units (that is, a one, a ten, a hundred, and so forth), and those above represent five. Beads are moved from the outer position toward the crossbeam when used to represent a number (Fig. 1).
By a series of motions using the thumb and forefinger, numbers may be added and subtracted. Addition and subtraction both work from left to right, in contrast to the usual method, using substantial mental arithmetic. For example, to add 384 + 795, the user begins with the beads positioned to represent 384 (Fig. 1). Then to add 795, one lower bead on the fourth rod from the right is moved up, while simultaneously moving the three beads on the third rod down (700 = 1000 − 300). Next, moving to the tens position, the user adds the 90 by the mental method of “add 100 and subtract 10,” thus moving one lower bead up on the hundreds rod and one lower bead down from the center on the tens rod. Finally, to add the 5, the user simply brings one of the upper beads down to the crosspiece. The result of the addition, 384 + 795 = 1179, then appears (Fig. 2).
Subtraction is done in a similar manner. In order to subtract 7 from any position, for example, the user subtracts 10 and adds 3. Both multiplication and division can also be performed with the help of the abacus, but these are much more complicated.
The abacus, in contrast to the electronic calculator, is simply an aid to mental computation. A well-developed facility with numbers is required in order to use it effectively. For this reason, it is the calculator of choice for teachers in the Far East. The advent of the electronic calculator, while a boon to the scientific community, may have little impact on shop owners who are comfortable with the abacus. See also: Calculators