Abacus

An abacus is a counting frame, typically wooden with balls sliding on wires.
It was first used before the adoption of the ten-digit Arabic numeral system
and is still widely used by small merchants in China.

Roman abacus

The Roman abacus contains seven long and seven shorter rods or bars, the
former having four perforated beads running on them and the latter one. This
figure of a Roman abacus is taken from an ancient monument:

The bar marked 1 indicates units, X tens, and so on up to millions. The
beads on the shorter bars denote fives,--five units, five tens, etc. The rod
O and corresponding short rod are for marking ounces; and the short quarter
rods for fractions of an ounce. Computations are made with it by means of
balls of bone or ivory running on slender bamboo rods, similar to the
simpler board, fitted up with beads strung on wires, which has been employed
in teaching the rudiments of arithmetic in English schools.

Chinese abacus

The Chinese abacus is usually around 20 cm (8 inches) tall and it comes in
various width depending on 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 round and made of hard wood. 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. The beads are counted by moving them up or down towards the beam.

Chinese abacus has functions other than counting. Unlike the simple counting
board used in elementary schools, very efficient suanpan techniques were
developed to do multiplication, division, addition, subtraction, square root
and cubic root at high speed.

Beads

The beads and rods were often lubricated to ensure speed. When all five
beads in the lower deck are moved up, they are reset to the original
position, and one bead in the top deck is moved down as a carry. When both
beads in the upper deck are moved down, they are reset and a bead on the
adjacent rod on the left is moved up as a carry. The result of the
computation is read off from the beads clustered near the separator beam
between the upper and lower deck.

Decimal system

In a sense, the abacus works as a 5-2-5-2 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, he simply adds another abacus to the left of
the row. In theory, the abacus can be expanded infinitely.

Modern decline in use

As recently as the late 1960s, abacus arithmetics were still being taught in
school, as in in Hong Kong; and into the 1990s in Taiwan. When handheld
calculators became popular, the schoolchildren's willingness of learn abacus
uses decreased dramatically. In the early days of handheld calculators, news
about abacus operators beating electronic calculator in arithmetics
competitions in both speed and accuracy often appeared in the media. The
main reason being that early calculators were often plagued by rounding and
overflow errors. While most handheld calculators can only handle 8 to 10
significant digits, the abacus is virtually limitless in precision.
Inexperienced operators might contribute to the loss too. But when
calculators' functionality improved, most Chinese realized that the abacus
could never compute complex functions -- such as trigonometry -- faster than
a calculator. The older generation -- mostly those who were born before the
early 1950s -- still used the abacus for a while, but electronic calculators
gradually displaced abacus in Hong Kong over the past four decades. As
calculators became more affordable, abacus is hardly seen in Hong Kong
nowadays. However, abacuses are still being used in China and Japan. The
slide rules also suffered a similar demise.

Miscellanea

The suanpan is closely tied to the Chinese "Hua1 Ma3" numbering system.

Japanese abacus

The Japanese eliminated one bead each from the upper and lower deck in each
column of the Chinese abacus, because these beads are redundent. That makes
the Japanese soroban more like the Roman abacus. The soroban is about
8 cm (3 inches) tall. The beans on a soroban are usually double cone shape.

Native American abacus

Many sources also mentioned use of abacus in ancient Mayan culture. The
Mesoamerican abacus is closely tied to the base-20 Mayan numerals system.

Uses by the visually impaired

Abaci are still used by individuals who have visual impairments. They use an
abacus to perform the mathematical functions multiplication, division,
addition, subtraction, square root and cubic root. A piece of soft fabric is
placed behind the beads so that they don't move inadvertantly. This keeps
the beads in place while a person feels the beads or uses the abacus.