Math in Computing

Mechanical and Electronic Calculating Devices

How did Gottfried Wilhelm von Leibniz advance calculating devices?

German mathematician and philosopher Gottfried Wilhelm von Leibniz (1646–1716) not only described the binary number system—a major concept of all modern computers—but also co-invented differential calculus and designed a machine that would perform the four basic arithmetic functions. By 1674 he had completed his design and commissioned the building of the Leibniz Stepped Drum, or the Stepped Reckoner, as he called his machine.

The device used a special type of gear named the Leibniz wheel (or stepped drum), a cylinder with nine bar-shaped teeth along a length parallel to the cylinder’s axis. As the cylinder was rotated with a crank, a ten-toothed wheel would rotate from zero to nine positions, depending on its position from the drum. The movements of the various mechanisms would be translated into multiplication or division, depending on what direction the stepped drum was rotated.

Although there were apparently only two prototypes of the device (both still exist), Leibniz’s design—along with Pascal’s—were the basis for most mechanical calculators in the 18th century. As with most such machines that could not be mass produced— much less understood by the masses—they were more curiosities for display than machines put to actual use.


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