nine’s complement

Articles

Inside Mechanical Calculators

May 1, 2018 by 25 Comments

For as busy as things can get at the grocery store on a typical afternoon just before the dinner hour, at least the modern experience has one thing going for it: it’s relatively quiet. Aside from the mumbled greetings and “Paper or plastic?” questions from the cashier, and the occasional screaming baby in the next aisle, the only sound you tend to hear is the beeping of the barcode scanner as your purchase is tallied up.

Jump back just 40 years and the same scene was raucous, with cashiers reading price tags and pounding numbers into behemoth electromechanical cash registers. Back then, if you wanted help with any arithmetic with more than just a few operations, some kind of mechanical calculator was your only choice. From simple “one-banger” adding machines to complex analog computers, mechanical devices were surprisingly capable data processing tools. Here’s a brief look at how some of the simpler ones worked.

Continue reading “Inside Mechanical Calculators” →

Retrotechtacular: Pascal Got Frustrated At Tax Time, Too

December 23, 2014 by 13 Comments

While necessity is frequently the mother of invention, annoyance often comes into play as well. This was the case with [Blaise Pascal], who as a teenager was tasked with helping his father calculate the taxes owed by the citizens of Rouen, France. [Pascal] tired of moving the beads back and forth on his abacus and was sure that there was some easier way of counting all those livres, sols, and deniers. In the early 1640s, he devised a mechanical calculator that would come to be known by various names: Pascal’s calculator, arithmetic machine, and eventually, Pascaline.

The instrument is made up of input dials that are connected to output drums through a series of gears. Each digit of a number is entered on its own input dial. This is done by inserting a stylus between two spokes and turning the dial clockwise toward a metal stop, a bit like dialing on a rotary phone. The output is shown in a row of small windows across the top of the machine. Pascal made some fifty different prototypes of the Pascaline before he turned his focus toward philosophy. Some have more dials and corresponding output wheels than others, but the operation and mechanics are largely the same throughout the variations.

Continue reading “Retrotechtacular: Pascal Got Frustrated At Tax Time, Too” →

Retrotechtacular: The CURTA Mechanical Calculator

September 16, 2014 by 39 Comments

The CURTA mechanical calculator literally saved its inventor’s life. [Curt Herzstark] had been working on the calculator in the 1930s until the Nazis forced him to focus on building other tools for the German army. He was taken by the Nazis in 1943 and ended up in Buchenwald concentration camp. There, he told the officers about his plans for the CURTA. They were impressed and interested enough to let him continue work on it so they could present it as a gift to the Führer.

This four-banger pepper mill can also perform square root calculation with some finessing. To add two numbers together, each must be entered on the digit setting sliders and sent to the result counter around the top by moving the crank clockwise for one full rotation. Subtraction is as easy as pulling out the crank until the red indicator appears. The CURTA performs subtraction using nine’s complement arithmetic. Multiplication and division are possible through successive additions and subtractions and use of the powers of ten carriage, which is the top knurled portion.

Operation of the CURTA is based on [Gottfried Leibniz]’s stepped cylinder design. A cylinder with cogs of increasing lengths drives a toothed gear up and down a shaft. [Herzstark]’s design interleaves a normal set of cogs for addition with a nine’s complement set. When the crank is pulled out to reveal the red subtraction indicator, the drum is switching between the two sets.

Several helper mechanisms are in place to enhance the interface. The user is prevented from ever turning the crank counter-clockwise. The crank mechanism provides tactile feedback at the end of each full rotation. There is also a lock that disallows switching between addition and subtraction while turning the crank—switching is only possible with the crank in the home position. There is a turns counter on the top which can be set to increment or decrement.

You may recall seeing Hackaday alum [Jeremy Cook]’s 2012 post about the CURTA which we linked to. A great deal of information about the CURTA and a couple of different simulators are available at curta.org. Make the jump to see an in-depth demonstration of the inner workings of a CURTA Type I using the YACS CURTA simulator.

Continue reading “Retrotechtacular: The CURTA Mechanical Calculator” →