An abacus is a calculation tool, often constructed as a wooden frame with beads sliding on wires. It was in use centuries before the adoption of the written Arabic numeral system and is still widely used by merchants and clerks in Russia, China and elsewhere.
The Late Roman abacus shown here contains seven long and seven shorter grooves, the former having up to five beads in each and the latter one.
The groove marked I indicates units, X tens, and so on up to millions. The beads in the shorter grooves denote fives—five units, five tens, etc., essentially in a bi-quinary coded decimal system. The short grooves on the right may have been used for marking Roman ounces.
Computations are made by means of beads which would have been slid up and down the grooves to indicate the value of each column.
The Chinese abacus is typically around 20 cm (8 inches) tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom. The beads are usually rounded and made of a hard wood. The beads are counted by moving them up or down towards the beam. The abacus can be reset to the starting position instantly by a quick jerk along the horizontal axis to spin all the beads away from the horizontal beam at the center.
Chinese abaci can be used for functions other than counting. Unlike the simple counting board used in elementary schools, very efficient swanpan techniques have been developed to do multiplication, division, addition, subtraction, square root and cube root operations at high speed.
Like the Roman abacus, this device works as a bi-quinary based number system in which carries and shiftings are similar to the decimal number system. Since each rod represents a digit in a decimal number, the computation capacity of the abacus is only limited by the number of rods on the abacus. When a mathematician runs out of rods, another abacus can be added to the left of the first. In theory, the abacus can be expanded indefinitely in this way.
As recently as the late 1960s, abacus arithmetic was still being taught in school in Hong Kong and into the 1990s in Taiwan. However, when handheld calculators became readily available, schoolchildren’s willingness to learn the use of the abacus decreased dramatically. In the early days of handheld calculators, news of abacus operators beating electronic calculators in arithmetic competitions in both speed and accuracy often appeared in the media (Early electronic calculators could only handle 8 to 10 significant digits, whereas the abacus is virtually limitless in precision.) But when the functionality of calculators improved beyond simple arithmetic operations, most people realized that the abacus could never compute higher functions – such as those in trigonometry – faster than a calculator. Nowadays, as calculators have become more affordable, the abacus is hardly seen in Hong Kong. Abaci are, however, still being used elsewhere in China and in Japan. Though abaci are not commonly used in Hong Kong and Taiwan, many parents still send their children to private tutor to learn abacus as a learning aid and stepping stones to faster and more accurate mental arithmetic skills.
Webarchive backup: Mesoamerican abacus (this site is no longer online - but the webarchive backup are; however, one of the author’s documents comparing the organization and use of the mesoamerican abacus and the chinese abacus is mirrored at [1]); see also [1]
The Chinese abacus is typically around 20 cm (8 inches) tall and it comes in various widths depending on the application. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom. The beads are usually rounded and made of a hard wood. The beads are counted by moving them up or down towards the beam. The abacus can be reset to the starting position instantly by a quick jerk along the horizontal axis to spin all the beads away from the horizontal beam at the center. 