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A training institute intends to give scholarships to its students as per the criteria given below …
A training institute intends to give scholarships to its students as per the criteria given below :
• The student has excellent academic record but is financially weak.
OR
• The student does not have an excellent academic record and belongs to a backward class.
OR
• The student does not have an excellent academic record and is physically impaired.
The inputs are:
(In all the above cases 1 indicates yes and 0 indicates no).
Output : X [1 indicates yes, 0 indicates no for all cases]
Draw the truth table for the inputs and outputs given above and write the SOP expression for $X(A,F,C,I)$.
| INPUTS | |
| A | Has excellent academic record |
| F | Financially sound |
| C | Belongs to a backward class |
| I | Is physically impaired |
Answer
Answer
AILet X=1 mean the student gets the scholarship. From the criteria: $X = A.F' + A'.C + A'.I$, where $A.F'$ means 'excellent record (A=1) but financially weak (F=0, i.e. NOT financially sound)', $A'.C$ means 'not an excellent record and belongs to a backward class', $A'.I$ means 'not an excellent record and is physically impaired'.
Truth table (columns A, F, C, I; verified with the boolean tool):
SOP expression: $X(A,F,C,I) = A.F' + A'.C + A'.I$
| A | F | C | I | X |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 1 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 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 | 0 |
| 1 | 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 | 0 |
From ISC 2018 Computer Science Paper 1, question 5(a).