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N-MODULAR REDUNDANCY In the previous chapter, parallel and standby systems were discussed as means of introducing redundancy and ways to improve system reliability. After the concepts were introduced, we saw that one of the complicating design features was that of the coupler in a parallel system and that of the decision unit and switch in a standby system. These complications are present in the design of analog systems as well as digital systems. However, a technique known as voting redundancy eliminates some of these problems by taking advantage of the digital nature of the output of digital elements | Reliability of Computer Systems and Networks Fault Tolerance Analysis and Design Martin L. Shooman Copyright 2002 John Wiley Sons Inc. ISBNs 0-471-29342-3 Hardback 0-471-22460-X Electronic 4 -MODULAR REDUNDANCY INTRODUCTION In the previous chapter parallel and standby systems were discussed as means of introducing redundancy and ways to improve system reliability. After the concepts were introduced we saw that one of the complicating design features was that of the coupler in a parallel system and that of the decision unit and switch in a standby system. These complications are present in the design of analog systems as well as digital systems. However a technique known as voting redundancy eliminates some of these problems by taking advantage of the digital nature of the output of digital elements. The concept is simple to explain if we view the output of a digital circuit as a string of bits. Without loss of generality we can view the output as a parallel byte 8 bits long . The concept generalizes to serial or parallel outputs n bits long. Assume that we apply the same input to two identical digital elements and compare the outputs. If each bit agrees then either they are both working properly likely or they have both failed in an identical manner unlikely . Using the concepts of coding theory we can describe this as an error-detection not an error-correction method. If we detect a difference between the two outputs then there is an error although we cannot tell which element is in error. Suppose we add a third element and compare all three. If all three outputs agree bitwise then either all three are working properly most likely or all three have failed in the same manner most unlikely . If two of the element outputs say one and three agree then most likely element two has failed and we can rely on the output of elements one and three. Thus with three elements we are able to correct one error. If two errors have occurred it is very possible that they will .

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