Building the Pascaline: Digital Computing Like It’s 1642 David S. Touretzky, Computer Science Department, Carnegie Mellon University

History Blaise Pascal created the first working mechanical calculator in 1642: the Pascaline. The machine could perform both addition and subtraction. The latter was accomplished using nines complement arithmetic. Over the next 20 years Pascal built 40 of these devices. Nine survive today.

Technology The backstop pawl ensured that an accumulator wheel was in one of 10 discrete states. The sautoir was an ingenious carry mechanism that worked by converting potential to kinetic energy.

Reproduction I developed a Pascaline model in SolidWorks. The parts are laser cut 1/8 inch acrylic, plus off the shelf aluminum standoffs and fasteners. Assembly requires just a screwdriver, pliers, and Loctite. The open source design can be customized by students to make their own Pascalines.

Discussion Topics • What makes a device “digital”? • How does nonlinearity produce discrete states in a continuous world? • How are nonlinearities induced in the Pascaline vs. in digital electronics? • How do the concepts “half adder” and “full adder” map onto the Pascaline? • Is the Pascaline really adding, or just counting? • How does the Pascaline use nines complement arithmetic to perform subtraction, and why isn’t it tens complement?

Open Source Kit

SolidWorks design files, laser-ready DXF files, and a parts list are here: http://www.cs.cmu.edu/~dst/Pascaline

Funded by a gift from Northrup Grumman.

See also: • How the Pascaline Works (video) www.youtube.com/watch?v=3h71HAJWnVU • Wikipedia : Pascal’s calculator.

Image taken from “How the Pascaline Works” (YouTube video) by The Visual Guide to Mechanical Computing.

Backstop pawl

Sautoir