note2 - CSCI 120 Introduction to Computation History of...

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Unformatted text preview: CSCI 120 Introduction to Computation History of computing (draft) Saad Mneimneh Visiting Professor Hunter College of CUNY 1 Early computing devices Counting is the most basic form of computing. In order to compute, we must count! Of course now that we have numbers, counting is implicit. But there was a time when numbers did not exist. So what is the earliest computing device? The answer: the fingers! In the old days, before numbers were invented, people used their fingers to count. As larger quantities started to emerge, i.e. larger than the ten fingers could represent, small objects like pebbles were used to help counting. In fact, thats why we still use 10 as the base for our natural number system. We have 10 digits only 0,1,2,3,4,5,6,7,8, and 9. Whenever we reach 10 fingers, thats a pebble. Therefore, 10 is a pebble and no fingers, 23 is two pebbles and 3 fingers, etc... People needed not only to count, but also to compute cost of goods, for instance in trading. Therefore, counting devices were invented to make everyday calculations. The abacus is one of the many counting devices invented to count large numbers. The history of the abacus has been traced as far back as the ancient Greek and Roman civilization, 500 B.C. The abacus as we know it today appeared around 1200 A.D. in china. This is the modern abacus. It is a device usually of wood (plastic in recent times) having a frame that holds rods with freely moving beads mounted on them. The following figure shows the modern abacus. Figure 1: Abacus The position of the beads represent numbers. This machine relies on a human operator to perform useful operations. The human must operate it by moving the beads. The abacus alone is merely a data storage device (or a representation device to represent numbers). The abacus is still in use to- day in some shops in Asia. For more information about the abacus and for a tutorial on how to use it for addition and other arithmetic operations, see http://www.ee.ryerson.ca/elf/abacus/ . Heres a basic description of how we represent numbers on an abacus. Instead of using fingers, pebbles, rocks, and mountains, etc... we need not have a physical entity associated with each cate- gory. We simply abstract or generalize and think about the units, the tens, the hundreds, the thousands, etc... Each of these categories correspond to one of the rods on the abacus. But each rod mimics a human being. Therefore, for each rod, the two beads on the upper part represent the two hands, and the five beads on the lower part represent the five fingers on each hand. Beads are moved towards the center to contribute their values. A bead from the lower part contributes a 1. A bead from the upper part contributes a 5. For instance, the following is a representation for the number 9876543210....
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This note was uploaded on 03/27/2010 for the course CSCI 120 taught by Professor Saadmneimneh during the Spring '09 term at CUNY Hunter.

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note2 - CSCI 120 Introduction to Computation History of...

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