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ECE354 hw4 - sol

ECE354 hw4 - sol - NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT...

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NEW JERSEY INSTITUTE OF TECHNOLOGY DEPT. OF ELECTRICAL & COMPUTER ENGINEERING ACADEMIC YEAR 2008-2009 SEMESTER 1 ECE354 DIGITAL TEST S OLUTION HW4 1. From HW3, the list of undetectable single stuck-at faults is: { } 1 / , 1 / , 1 / , 0 / , 1 / 9 7 4 4 2 g g g g g We need to inject the faults, one by one, reducing the circuit as we go, until we get an irredundant circuit. We start with a fault closest to the output. There are two candidates for this: { } 1 / , 1 / 9 7 g g . We choose to start with 1 / 7 g . Fig. 1 shows the reduced circuit resulting from the injection of 1 / 7 g . A B C D F' 1 g 2 g 3 g 4 g 5 g 6 g 8 g 9 g 10 g 11 g Fig. 1. Reduced circuit after the injection of g 7/1 Notice that several lines have merged after this reduction. For example, line 5 g is the same as line 10 g . To check whether or not this circuit is irredundant, we check whether 1 / 9 g is still undetectable in this new circuit. We have: AB CD g F + = 9 ' , D B g + = 9 CD AB g CD g AB g F = = 9 9 9 ) ( ' , 0 ' 9 9 = = + = CD AB D B CD AB D B g F g Therefore, 1 / 9 g is still undetectable. We proceed to inject this fault and reduce the circuit again (see Fig. 2). 1

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A B C D F' ' 1 g 3 g 5 g 6 g 8 g 10 g 11 g Fig. 2. Reduced circuit after the injection of g9 /1 Since the circuit of Fig. 2 is fanout-free, it is irredundant. Notice, however, that it is not minimal! It implements the same Boolean function as F , i.e. F CD B A CD AB F = + + = + = ' ' . 2. Fig. 3 shows the propagation of ABCD =0000. A B C D F 1 g 2 g 3 g 4 g 5 g 6 g 7 g 8 g 9 g 10 g 11 g 0 1 0 0 0 0 1 1 1 1 Fig. 3. Propagation of ABCD =0000 The faults covered by ABCD =0000 is { } 0 / F .
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