Building the Pascaline: Digital Computing Like It's 1642 (Abstract Only)

The Pascaline was the first working mechanical calculator, created in 1642 by the French polymath Blaise Pascal. Over the next two decades Pascal built 40 of these machines, of which nine survive today. Several good web resources describe the Pascaline, but to properly appreciate the sautoir, Pascal's kinetic energy solution to jam-free ripple carry, building a working replica is invaluable. Thanks to the growing availability of rapid prototyping tools, it has become relatively easy for CS educators to fabricate physical artifacts to help students explore computational ideas. I've created a Pascaline kit using laser-cut acrylic and standard fasteners that can be assembled with just a screwdriver, pliers, and Loctite. High school or college students with minimal skills can put it together in a few hours and have a functioning calculator. Exploring the Pascaline's design is an engaging way to connect a milestone in the early history of computing with more modern theoretical concepts. Students can investigate questions such as: What makes a device "digital"? (Slide rules have numeric scales but are analog devices.) How does nonlinearity produce discrete states in a continuous world? How are nonlinearities induced in the Pascaline vs. in digital electronics? How do the logic design concepts "half adder" and "full adder" map onto the components of the Pascaline? Is the Pascaline really adding, or merely counting? How does the Pascaline use nines complement arithmetic to perform subtraction, and why isn't it tens complement? The Pascaline kit, designed in SolidWorks, is open source and available at http://www.cs.cmu.edu/~dst/Pascaline.