A line L in a circuit is said to have a stuck-at-0 fault if the line…
2005
A line L in a circuit is said to have a stuck-at-0 fault if the line permanently has a logic value 0. Similarly a line L in a circuit is said to have a stuck-at-1 fault if the line permanently has a logic value 1. A circuit is said to have a multiple stuck-at fault if one or more lines have stuck at faults. The total number of distinct multiple stuck-at faults possible in a circuit with N lines is
- A.
3^N
- B.
3^N - 1
- C.
2^N - 1
- D.
2
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Correct answer: B
For each line there are three possibilities: stuck-at-0, stuck-at-1, or no fault.
Total combinations for N lines = 3^N (three choices per line).
The case where every line is fault-free (no stuck-at faults) is included in 3^N and must be excluded because a multiple stuck-at fault requires one or more lines to be faulty.
Therefore the number of distinct multiple stuck-at faults = 3^N - 1.
Example: For N = 1 there are 2 faults (stuck-at-0 and stuck-at-1) = 3^1 - 1. For N = 2 there are 8 faults = 3^2 - 1.
Note: The expression 2^N - 1 would count only which non-empty sets of lines are faulty but would not distinguish the two possible stuck values per faulty line, so it undercounts the possibilities.