Pascaline Calculator

By Lana Wehbeh

The Pascaline, also known as Pascal’s Calculator or the Arithmetic Machine, was invented in 1942 by Blaise Pascal at the young age of 18 years old. The Pascaline was primarily an adding machine, with its initial form supporting up to five digits, but with later versions going up to 10. It also didn’t initially support decimal places but later would. The Pascaline itself was fairly small and portable, about the size of a shoebox being 36 cm long, 13 cm wide, and 8 cm high. For comparison, the stepped drum calculator of 1673 was 97x30x25 cm, a significant increase in size.

The Pascaline used dials that allowed users to input numbers. Its basic function was addition, as the user would turn the dials to input a number, then enter another number using the same dials to add the two numbers, the result of which would then be displayed. The Pascaline itself was notable for its controlled carry mechanism, wherein the addition of anything to a 9 would change that place value to a zero then carry the rest onto the next place value.

Subtraction was more difficult, as it could only be accomplished using the implementation of the nines complement. Whether manually or by using the machine, you would find the nines complement for each digit in the number you wish to subtract, so if I was subtracting 30, the nines complement would be 69. You could then add the nines complement to the other number so if i was subtracting 30 from 50, I would add 69 to 50, to get a total of 119. The final step would be to mentally add the first digit of the result to the rest of the digits to get your final answer. In this case I would add 1 to 19 to get a final answer of 20. The process itself was tedious, which is why the Pascaline is often touted as only efficient for addition.

To reset the machine, the controlled carry mechanism was used. By setting all the dials to 9 and then adding 1 to the first (rightmost) dial, the user creates a domino effect that resets every place value to a zero. The Pascaline could also do multiplication or division through what was essentially repeated addition or subtraction but it was mostly inefficient. It was also rather delicate and could give incorrect results if not handled delicately or bumped slightly as the mechanisms were easily triggered.

The Pascaline itself has gone down in history because of its many accomplishments as the only operational mechanical calculator in the 1600s, the first with an effective controlled carry mechanism, and the first business machine and one to be used in an office.

Works Cited

“Blaise Pascal — First Digital Calculating Machine.” Blaise Pascal — First Digital Calculating Machine | Educalc.net, www.educalc.net/196488.page.

“Pascal’s Calculator.” Wikipedia, Wikimedia Foundation, 9 May 2022, en.wikipedia.org/wiki/Pascal’s_calculator.

“Pascaline.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., www.britannica.com/technology/Pascaline.

Walker, Johnnie. “About Pascaline.” Pascal’s Adder — About Pascaline, www.macs.hw.ac.uk/~greg/calculators/pascal/About_Pascaline.htm.

“What Is Pascal’s Calculator ?” GeeksforGeeks, 19 Jan. 2021, www.geeksforgeeks.org/what-is-pascals-calculator/.