Earliest true hardware

Devices have been used to aid computation for thousands of years, mostly 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 calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in containers.^[3][4] The use of counting rods is one example.
The abacus was early used for arithmetic tasks. What we now call 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 European 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.

Several 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 earliest known mechanical analog computers.^[5] Hero of Alexandria (c. 10–70 AD) made many complex mechanical devices including automata and a programmable cart.^[6] Other early versions of mechanical devices used to perform one or another 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.

Suanpan (the number represented on this abacus is 6,302,715,408)

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.^[7] 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.^[8] Slide rules were used by generations of engineers and other mathematically involved professional workers, until the invention of the pocket calculator.^[9]

Yazu Arithmometer. Patented in Japan in 1903. Note the lever for turning the gears of the calculator.

Wilhelm Schickard, a German polymath, designed a calculating clock in 1623. It made use of a single-tooth gear that was not an adequate solution for a general carry mechanism.^[10] A fire destroyed the machine during its construction in 1624 and Schickard abandoned the project. Two sketches of it were discovered in 1957, too late to have any impact on the development of mechanical calculators.^[11]
In 1642, while still a teenager, Blaise Pascal started some pioneering work on calculating machines and after three years of effort and 50 prototypes^[12] he invented the mechanical calculator.^[13][14] He built twenty of these machines (called Pascal's Calculator or Pascaline) in the following ten years.^[15] Nine Pascalines have survived, most of which are on display in European museums.^[16]
Gottfried Wilhelm von Leibniz invented the Stepped Reckoner and his famous cylinders around 1672 while adding direct multiplication and division to the Pascaline. 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."^[17]
Around 1820, Charles Xavier Thomas de Colmar created the first successful, mass-produced mechanical calculator, the Thomas Arithmometer, that could add, subtract, multiply, and divide.^[18] 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,^[19] a central ingredient of all modern computers. However, up to the 1940s, many subsequent designs (including Charles Babbage's machines of the 1822 and even ENIAC of 1945) were based on the decimal system;^[20] ENIAC's ring counters emulated the operation of the digit wheels of a mechanical adding machine.
In Japan, Ryōichi Yazu patented a mechanical calculator called the Yazu Arithmometer in 1903. 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.^[21] More than 200 units were sold, mainly to government agencies such as the Ministry of War and agricultural experiment stations.^[22][23]