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Fault Detection:

Let x1,x2,x3................xn be the inputs to a combinational circuit in the presence of fault k. As an example consider the circuit may be either stuck at zero (s-a-0) or stuck at one (s-a-1). We shall denote by m0 and m1 the faults of wire m s-a-0 and s-a-1 respectively. Similar notation is used for the other wires. The truth table for this circuit is shown in figure(b). Where coulmn f denotes the fault free output while, for example coulmns f(m0) and f(m1) corresponed ,respectively to the circuit output in the presence of faults m0 and m1 and so on. An input combination is referred to as a test for fault fk if , in response to that input combination, the output of the correctly operating circuit is different from that of the circuit impaired by fault fk . Hence , for example ,the input combination 111 is the only test for detecting the fault , f(m0) in the circuit of figure(c) . Since it is the only input combination for which the value in the coulmn f and f(m0///0 are different . n the other hand , fault f(q1) can be detected by the tests 001,011,and 101 and so on,for other faults. More precisely , an input combination a1,a2,a3,a4.....aN is a test for detecting fault fk if and only if f(a1,a2,a3....aN) fk(a1,a2,a3,.....aN)=1 where f (a1,a2,a3..aN) and fk(a1,a2,a3,.........aN) denote respectively the fault free output and the incorrect output in response to the input a1,a2,a3,....aN .Thus in order to determine all the tests that detect a fault fk , it is necessary to take the modulo-2 sum of coulmn f and fk in the truth table.
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