Gottfried Wilhelm Leibniz and his calculating machine report

Gottfried Wilhelm Leibniz and his calculating machine report by Torsten Brandes 1

Chapter 1 • Construction of mechanical calculating machines 2

Structure of a mechanical calculating machine • counting mechanism two counting wheels 3

counting mechanism • Every counting wheel represents a digit. • By rotating in positive direction it is able to add, by rotating in negative direction it is able to subtract. • If the capacity of a digit is exceeded, a carry occurs. • The carry has to be handed over the next digit. 4

counting mechanism S – lever Zi – toothed wheel dealing with the carry between two digits 5

Chapter 2: calculating machines bevore and after Leibniz • 1623 Wilhelm Schickard developes a calculating machine for all the four basic arithmetic operations. It helped Johann Kepler to calculate planet‘s orbits. • 1641 Blaise Pascal developes an adding- and subtracting machine to maintain his father, who worked as a taxman. • 1670 - 1700 Leibniz is working on his calculator. • 1774 Philipp Matthäus Hahn (1739 -1790) contructed the first solid machine. 6

Leibniz‘ calculating machine. • Leibniz began in the 1670 to deal with the topic. • He intended to construct a machine which could perform the four basic arithmetic operations automatically. • There where four machines at all. One (the last one) is preserved. 7

stepped drum A configuration of staggered teeth. The toothed wheel can be turned 0 to 9 teeth, depending of the position of this wheel. 8

four basic operations performing machine by Leibniz 9

Skizze drawing: W. Jordan • H – crank • K – crank for arithmetic shift • rotation counter 10

Functionality • Addition: partitioning in two tacts 1. Addition digit by digit, saving the occuring carries with a toothed wheel. 2. Adding the saved carries to the given sums, calculated before. 11

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Subtraction. • Similar to adding. • The orientation of rotating the crank has to be turned. 13

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Multiplication (excampel) • • 1. 2. 3. 4. 5. 6. was possible by interated additions 32. 448*75 Input of 32. 448 in the adjusting mechanism. Input of 5 in the rotation counter. Rotating the crank H once. The counting mechanism shows 162. 240. Rotating the crank K. The adjusting mechanism is shifted one digit left. Input of 7 in the rotation counter. Rotating the crank H once. The counting mechanism shows 2. 433. 600. 15