# Fault Diagnosis and Fault Tolerance: A Systematic Approach by Tinghuai Chen

By Tinghuai Chen

With the quick development of integration scale of VLSI chips and the current desire for trustworthy desktops in area exploration, fault analysis and fault toleran ce became extra very important than ahead of, and accordingly display loads of curiosity ing issues which magnetize many researchers to make lots of contribu tions to this box. lately, many new and demanding effects were accomplished. a short test over the lawsuits of the meetings on fault tolerant computing and layout automation in addition to on checking out will persuade the reader of that. yet regrettably those achievements haven't been complete ly mirrored within the textbooks, in order that there seems a niche for the hot researcher who already has the elemental wisdom and desires to start examine during this quarter. As a treatment for this deficiency, this e-book is meant for commence ners, specifically graduate scholars, as a textbook that allows you to cause them to the frontier of a few branches of the fault-tolerant computing box. the 1st bankruptcy introduces the four-valued good judgment B4 and its applica tions. In 1966 Roth first proposed this four-valued good judgment as a method to generate checks for logical circuits, yet this paintings didn't situation the mathe matical foundation of B4 itself.

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**Sample text**

Xn} be any boolean functions on B~. xn} is called a boolean 23 equation on B~. tn ). •••. t n ) is called a solution of the boolean equation. Our goal is to find all the solutions of a given boolean equation. 8 x 1 o x 2 = D is a boolean equation. 1 we can list out its solutions Xl = 1. x 2 = D; Xl = x 2 D. 52) or Xl 'x2 + Xl 'x2 + Xl 'x2 = . Its corresponding solutions are 11* ** I x* 1 'x2 = x 1 'x2 = x 1 'x2 = • the same as above only in component form. 52) as the solution of the boolean equation.

7, g is represented by a square and gh is represented by a circle which lies in the square. Of course the sum of them is the square itself. But here the tests 1 ~ 0 1 II Fig. 7 Simplification g and gh correspond to two classes of faults which could be detected by the tests. Obviously the smaller term gh can detect both classes of faults. Therefore when we derive tests, the absorption law should be replaced by the inverse absorption law : g + gh = gh. This principle is also applicable to derive tests using F*, only beware that F* and F" are not in symmetry if the inverse absorption law is used.

When the circuit is normal and when the input values change. any wire y of the circuit (y may be the output wire F or an input wire Xi) can take the value 'I' and the value '0'. (the special cases F = 1 and F = 0 constantly are excluded). But when a physical defect occurs at y under some circumstances such that y can take only one value. then we say that a stuck-at fault occurs at y. The fault that y is stuck at 'I' is denoted by y s-a-l (or y~l). and the fault y stuck at '0' is denoted by y s-a-O (y~).