Earliest Calculators

Devices have been used to aid computation for thousands of years, using one-to-one correspondence with our fingers. The earliest counting device was probably a form of tally stick. Later record keeping aids throughout the Fertile Crescent included clay shapes, which represented counts of items, probably livestock or grains, sealed in containers. The abacus was used for arithmetic tasks. The Roman abacus was used in Babylonia as early as 2400 BC. Since then, many other forms of reckoning boards or tables have been invented. In a medieval counting house, a checkered cloth would be placed on a table, and markers moved around on it according to certain rules, as an aid to calculating sums of money (this is the origin of "Exchequer" as a term for a nation's treasury).

A number of analog computers were constructed in ancient and medieval times to perform astronomical calculations. These include the Antikythera mechanism and the astrolabe from ancient Greece (c. 150–100 BC), which are generally regarded as the first mechanical analog computers.Other early versions of mechanical devices used to perform some type of calculations include the planisphere and other mechanical computing devices invented by Abū Rayhān al-Bīrūnī (c. AD 1000); the equatorium and universal latitude-independent astrolabe by Abū Ishāq Ibrāhīm al-Zarqālī (c. AD 1015); the astronomical analog computers of other medieval Muslim astronomers and engineers; and the astronomical clock tower of Su Song (c. AD 1090) during the Song Dynasty.

The "castle clock", an astronomical clock invented by Al-Jazari in 1206, is considered to be the earliest programmable analog computer. It displayed the zodiac, the solar and lunar orbits, a crescent moon-shaped pointer travelling across a gateway causing automatic doors to open every hour, and five robotic musicians who play music when struck by levers operated by a camshaft attached to a water wheel. The length of day and night could be re-programmed every day in order to account for the changing lengths of day and night throughout the year.

Scottish mathematician and physicist John Napier noted multiplication and division of numbers could be performed by addition and subtraction, respectively, of logarithms of those numbers. While producing the first logarithmic tables Napier needed to perform many multiplications, and it was at this point that he designed Napier's bones, an abacus-like device used for multiplication and division. Since real numbers can be represented as distances or intervals on a line, the slide rule was invented in the 1620s to allow multiplication and division operations to be carried out significantly faster than was previously possible. Slide rules were used by generations of engineers and other mathematically inclined professional workers, until the invention of the pocket calculator. The engineers in the Apollo program to send a man to the moon made many of their calculations on slide rules, which were accurate to three or four significant figures.

German polymath Wilhelm Schickard built the first digital mechanical calculator in 1623, and thus became the father of the computing era. Since his calculator used techniques such as cogs and gears first developed for clocks, it was also called a 'calculating clock'. It was put to practical use by his friend Johannes Kepler, who revolutionized astronomy when he condensed decades of astronomical observations into algebraic expressions. An original calculator by Pascal (1640) is preserved in the Zwinger Museum. Machines by Blaise Pascal (the Pascaline, 1642) and Gottfried Wilhelm von Leibniz (1671) followed. Leibniz once said "It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used."

Around 1820, Charles Xavier Thomas created the first successful, mass-produced mechanical calculator, the Thomas Arithmometer, that could add, subtract, multiply, and divide. It was mainly based on Leibniz' work. Mechanical calculators, like the base-ten addiator, the comptometer, the Monroe, the Curta and the Addo-X remained in use until the 1970s. Leibniz also described the binary numeral system, a central ingredient of all modern computers. However, up to the 1940s, many subsequent designs (including Charles Babbage's machines of the 1800s and even ENIAC of 1945) were based on the decimal system; ENIAC's ring counters emulated the operation of the digit wheels of a mechanical adding machine.

In Japan, Ryoichi Yazu patented a mechanical calculator called the Yazu Arithmometer in 1902. It consisted of a single cylinder and 22 gears, and employed the mixed base-2 and base-5 number system familiar to users to the soroban (Japanese abacus). Carry and end of calculation were determined automatically. More than 200 units were sold, mainly to government agencies such as the Ministry of War and agricultural experiment stations. Yazu invested the profits in a factory to build what would have been Japan's first propeller-driven airplane, but that project was abandoned after his untimely death at the age of 31.