the operator can see either the number stored in the calculator or the complement of its value. Subtractions are performed like additions using some properties of 9's complement arithmetic. 9's complement The 9's complement of any one-digit decimal number d is 9-d. So the 9's complement of 4 is 5 and the 9's complement of 9 is 0. Similarly, the 11's complement of 3 is 8. In a decimal machine with n dials the 9's complement of a number A is: and therefore the 9's complement of (A-B) is: In other words, the 9's complement of the difference of two numbers is equal to the sum of the 9's complement of the minuend added to the subtrahend. The same principle is valid and can be used with numbers composed of digits of various bases (base 6, 12, 20), like in the surveying or the accounting machines. This can also be extended to: This principle applied to the Pascaline: Resetting the machine The machine has to be re-zeroed before each new operation. To reset his machine, the operator has to set all the wheels to their maximum, using the marks on two adjacent spokes, and then add 1 to the rightmost wheel. The method of re-zeroing that Pascal chose, which propagates a carry right through the machine, is the most demanding task for a mechanical calculator and proves, before each operation, that the machine is fully functional. This is a testament to the quality of the Pascaline because none of the 18th century criticisms of the machine mentioned a problem with the carry mechanism and yet this feature was fully tested on all the machines, by their resets, all the time. Addition Additions are performed with the display bar moved closest to the edge of the machine, showing the direct value of the accumulator. After re-zeroing the machine, numbers are dialed in one after the other. The following table shows all the steps required to compute 12,345 + 56,789 = 69,134 Subtraction Subtractions are performed with the display bar moved closest to the center of the machine showing the complement value of the accumulator. The accumulator contains during the first step and after adding B. In displaying that data in the complement window, the operator sees which is A and then which is . It feels like an addition since the only two differences in between an addition and a subtraction