Abacus in the context of "Numerical base"

Ancient Chinese scientists and engineers made significant scientific innovations, findings and technological advances across various scientific disciplines including the natural sciences, engineering, medicine, military technology, mathematics, geology and astronomy.

Among the earliest inventions were the abacus, the sundial, and the Kongming lantern. The Four Great Inventions – the compass, gunpowder, papermaking, and printing – were among the most important technological advances, only known to Europe by the end of the Middle Ages 1000 years later. The Tang dynasty (AD 618–906) in particular was a time of great innovation. A good deal of exchange occurred between Western and Chinese discoveries up to the Qing dynasty.

Bi-quinary coded decimal is a numeral encoding scheme used in many abacuses and in some early computers, notably the Colossus. The term bi-quinary indicates that the code comprises both a two-state (bi) and a five-state (quinary) component. The encoding resembles that used by many abacuses, with four beads indicating the five values either from 0 through 4 or from 5 through 9 and another bead indicating which of those ranges (which can alternatively be thought of as +5).

Several human languages, most notably Fula and Wolof also use biquinary systems. For example, the Fula word for 6, jowi e go'o, literally means five [plus] one. Roman numerals use a symbolic, rather than positional, bi-quinary base, even though Latin is completely decimal.

The Ancient Romans developed the Roman hand abacus, a portable, but less capable, base-10 version of earlier abacuses like those that were used by the Greeks and Babylonians.

Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus.

Babylonian cuneiform numerals, also used in Assyria and Chaldea, were written in cuneiform, using a wedge-tipped reed stylus to print a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record.

The Babylonians, who were famous for their astronomical observations, as well as their calculations (aided by their invention of the abacus), used a sexagesimal (base-60) positional numeral system inherited from either the Sumerian or the Akkadian civilizations. Neither of the predecessors was a positional system (having a convention for which 'end' of the numeral represented the units).

Pope Sylvester II (Latin: Silvester II; c. 946 – 12 May 1003), originally known as Gerbert of Aurillac, was a scholar and teacher who served as the bishop of Rome and ruled the Papal States from 999 to his death. He endorsed and promoted study of Moorish and Greco-Roman arithmetic, mathematics and astronomy, reintroducing to Western Christendom the abacus, armillary sphere, and water organ, which had been lost to Latin Europe since the fall of the Western Roman Empire. He is said to be the first in Christian Europe (outside of Al-Andalus) to introduce the decimal numeral system using the Hindu–Arabic numeral system.

The soroban (算盤, そろばん; counting tray) is an abacus developed in Japan. It is derived from the ancient Chinese suanpan, imported to Japan in the 14th century. Like the suanpan, the soroban is still used today, despite the proliferation of practical and affordable pocket electronic calculators.

The counting board is the precursor of the abacus, and the earliest known form of a counting device (excluding fingers and other very simple methods). Counting boards were made of stone or wood, and the counting was done on the board with beads, pebbles etc. Not many boards survive because of the perishable materials used in their construction, or the impossibility to identify the object as a counting board. The counting board was invented to facilitate and streamline numerical calculations in ancient civilizations. Its inception addressed the need for a practical tool to perform arithmetic operations efficiently. By using counters or tokens on a board with designated sections, people could easily keep track of quantities, trade, and financial transactions. This invention not only enhanced accuracy but also fueled the development of more sophisticated mathematical concepts and systems throughout history.

The counting board does not include a zero, as we have come to understand it today. It primarily used Roman numerals to calculate. The system was based on a base ten or base twenty system, where the lines represented the bases of ten or twenty, and the spaces representing base fives.