| ARITHMETIC BY MACHINE | ||||||||||||
| The Electric Abacus can do arithmetic as well as logic. And it can exercise control over the results of the input which sets the switching of those light bulbs in motion. That being so, it exercises the arithmetic, logic, control functions of a modern computer's CPU. | ||||||||||||
| THE CHINESE ABACUS | ||||||||||||
| There are various sizes to the abacus used in China, Japan and other countries. But here is a typical unit of the Chinese abacus. It has 9 rods and 7 beads. On each rod there is a separation into lower and upper beads by a bar, with 5 beads lower and 2 upper. ALL ARITHMETIC IS DONE BY REPOSITIONING THE BEADS: position-in and position-out. If all beads can be positioned in and out that yields 5x2x9=90 possible values or bits for the lower set and 2x2x9=36 bits for the upper beads. This is a 126 bit calculating machine. Give it enough beads and rods and the abacus can do any arithmetic problem in the hands of a skilled user, including square roots, cube roots etc. and decimal location. In skilled hands it is a speedy device. A story is told, whether folklore or not, about a contest in post-war Japan between General MacArthur's best clerk with the best mechanical calculator of the USM and the best abacus clerk in Japan. The abacus clerk won as the story goes; and that outcome is quite plausible. The mechanical devices used for calculating as above underwent a transformation and became electro-mechanical. What if the abacus had done the same? |
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| JUST ADD ELECTRICITY | ||||||||||||
| Given that the abacus bases all of its calculations on bead-in-position and bead-out-of-position, why not substitute light-on and light-off? In other words, a socket holds the position and the two binary values are expressed by light on (arbitrarily "1") and light off (arbitrarily "0"). Of course switch on and switch off works as well but the light bulb helps us to visualize the process. Given this configuration we do not need spaces on rods for moving beads in and out. The sockets or positions can be side by side. But the same principles apply. The principles have to do with a way of reading the bead or light pattern which corresponds to any number which is one set of rules and another set of rules for the arithmetic operation. ALL OF THESE RULES ENTAIL VARIATIONS ON SWITCHING OF BINARY VALUES. Thus the beads are positioned and read which is Input. Then the second set of rules is applied to perform the operation and the Output is read again in the same way as the input. So let's imagine one or more abacus for Input; one or more for operations and one or more for Output. As long as they are wired correctly, using simple series and parallel wirings, the wired connections will do what an army of abacus clerks could do to apply the rules of bead operations in a small fraction of the time. There could be master switches to this nest of wires and light bulbs as well. For example, one master switch might activate an abacus set wired for addition, another for square roots and so on. For both logic and arithmetic operations the benefits of wiring a network of abacuses are those of speed and accuracy. As the size or length of the procedures increases, the benefits will become more obvious. What about the "control" function of the CPU? The Electric Abacus can substitute here as well. For example, why not add a keyboard instead of setting beads or lightbulbs as Input? The keyboard could connect to the Input abacuses and set the input values automatically as wired. Similarly the Output abacus could be wired to an ouput display to substitute for a monitor. Imagine even a bank of light bulbs again for a display. If the number 5 is the output or answer of the Output abacus, it will connect to a display of light bulbs which will have a configuration shaped like the character 5. And all of might seem to be pure control of I/O rather than the usual arithmetic or logic application but control could also be called a kind of logic, ie "If-Then Logic". Allen Wyatt tells us in "Writing Your First Computer Program" "The If_______Then______structure is perhaps the most used of any programming structure". (IDG Books, 2000, page 103). STORAGE and MEMORY What do we need now to complete our primitive electro-mechanical computer other than a building the size of the Pentagon? Storage of bits? No problem. Just add as many electric abacuses as you want. What about memory so that programs can be applied at will? Why not wire in some special abacuses reserved for that purpose? Other abacuses would be set aside for straight-forward arithmetic and logic problems. But memory abacus devices could also be used. For example suppose the program requires having numbers "inputted" after a machine prompt and then a running total calculated with an output display? No problem. Just instruct the machine to first use its control capability to display "Type in a number". Then throw a switch to activate the addition memory abacus which performs the addition operation and displays the result along with a new prompt: "Type in another number". Then the addition is repeated as well as the operation and ouput. The result is a machine, the Electric Abacus, which substitutes for a 30 ton Mark I although it might weigh 300 tons but it would be a real computer nevertheless. If wiring ingenuity cannot solve the problems of the huge size, imagine the processing units as literally taking up the Pentagon Courtyard. All around the perimeter are the Input/Output keyboard-switching units and 1,000 clerks sit there in constant walkie-talkie communication to relay results back and forth so that the steps in calculating and programming can be adhered to. http://www.geocities.com/ELECTRIC_ABACUS/page5 |
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