2011_Fall_midterm_solution

2011_Fall_midterm_solution - 1 UNIVERSITY OF CALIFORNIA...

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1 UNIVERSITY OF CALIFORNIA Santa Barbara Department of Electrical and Computer Engineering ECE255A Fall 2011 MID-TERM EXAMINATION Name: __Solutions_____________________________ PERM: ____________________________ Note: Open book, open notes Problem Number Weight Score 1. 14 _________________ 2. 6 _________________ 3. 8 _________________ 4. 6 _________________ 5. 4 _________________ 6. 5 _________________ 7. 6 __________________ 8. 10 __________________ 9. 4 __________________ 10. 5 __________________ ___________________________________________________________________ Total 68 __________________
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2 1. (14 pts.) Consider the following circuit. (a) (6 pts.) Determine the fault equivalences among the three faults, H s-a-0, J s-a-0, and K s-a-0. That is, are these three faults equivalent? If not, is any pair of these three faults equivalent? Prove your answer. (b) (4 pts.) Using the parallel fault simulation algorithm (assuming a four-bit machine word), determine which of the three single faults, F s-a-1, H s-a-1, and L s-a-0, are detected by the input vector A=1; B=0. (c) (4 pts.) Using Parallel-Pattern Single-Fault Propagation algorithm (assuming a four-bit machine word), determine which of the four vectors (i.e. AB={00, 01, 10, 11}) of this circuit can detect F s-a-1. Comparing the responses of these two simulations, we can conclude vector AB={10} detects F s-a-1.
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3 2. (6 pts.) Write the Conjunctive Normal Form (CNF), F , for the following three-input function whose inputs are a , b , and c , and output is z: a b c z 0 x x 1 1 0 x 0 1 1 0 0 1 1 1 1 F ( a, b, c, z )= 3. (8 pts.) Consider the transition faults for a 2-input AND gate whose inputs are
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2011_Fall_midterm_solution - 1 UNIVERSITY OF CALIFORNIA...

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