GATE | Gate IT 2005 | Question 46

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


Answer: (B)

Explanation:
In a line, there can be three possibilities :
1. Stuck-at 0 fault
2. Stuck-at 1 fault
3. No fault

Thus, total combinations = 3N

It is mentioned that one or more lines have stuck at faults.
So, a case in which there is no fault in any line i.e. all lines are correct can not occur.
Total combinations = 3N – 1

 
Thus, option (B) is correct.

 
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