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Post pandemic, to encourage the tourism industry in India, the Ministry of Tourism started a policy…
Post pandemic, to encourage the tourism industry in India, the Ministry of Tourism started a policy in which a tourist would be allowed to book a resort at a rebate, if any one of the following criteria matches.
● The tourist has an AADHAR card and has no criminal record.
● The tourist is the government employee and has repeated the resort visit in a span of six months.
● The tourist has an AADHAR card and has repeated the resort visit in a span of six months.
Inputs:
- A: The tourist has an AADHAR CARD
- C: The tourist has a criminal record
- G: The tourist is the government employee
- V: The tourist has repeated the resort visit in a span of six months
Output:
- F: The tourist would be allowed to book the resort at rebate. [1 indicates Yes and 0 indicates No].
Draw the truth table for inputs and outputs given above and write the Cardinal Sum of product expression for $F(A, C, G, V)$.
Answer
Answer
AIF = A.C' + G.V + A.V (A: has AADHAR, C: has criminal record, G: govt employee, V: repeated visit in 6 months)
Truth table:
Cardinal (sum-of-minterms) sum-of-products: $F(A,C,G,V) = \Sigma(3,7,8,9,10,11,13,15)$
| A | C | G | V | F |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
From ISC Computer Science - Competency Focused Practice Questions (CISCE, August 2024), question 70.
Check your working with the Boolean algebra solver: the steps law by law, the K-map and the logic circuit for any expression.