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A superhero is allowed access to a secure Avengers facility if he / she meets any of the following…
A superhero is allowed access to a secure Avengers facility if he / she meets any of the following criteria:
• The superhero has Avengers’ membership and possesses a high-security clearance badge
OR
• The superhero does not have Avengers membership but holds a special permit issued by S.H.I.E.L.D. along with a high-security clearance badge
OR
• The superhero is not a recognised ally but holds a special permit issued by S.H.I.E.L.D. along with a high-security clearance badge
The inputs are:
(In all the above cases, 1 indicates YES and 0 indicates NO)
Output: X – Denotes allowed access [1 indicates YES and 0 indicates NO in all cases]
Draw the truth table for the inputs and outputs given above. Write the POS expression for X (A, S, C, L).
| INPUTS | |
| A | Superhero has Avengers membership. |
| S | Superhero holds a special permit issued by S.H.I.E.L.D. |
| C | Superhero possesses a high-security clearance badge |
| L | Superhero is a recognised ally |
Answer
Answer
AIX = A.C + A'.S.C + L'.S.C
(access allowed when: has membership AND clearance; OR lacks membership but has a SHIELD permit AND clearance; OR is not a recognised ally but has a SHIELD permit AND clearance)
Truth Table:
POS expression (product of maxterms where X=0, in order A,S,C,L):
$X(A,S,C,L) = (A+S+C+L)(A+S+C+L')(A+S+C'+L)(A+S+C'+L')(A+S'+C+L)(A+S'+C+L')(A'+S+C+L)(A'+S+C+L')(A'+S'+C+L)(A'+S'+C+L')$
| A | S | C | L | X |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
From ISC 2025 Computer Science Paper 1, question 3(i).