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A Football Association coach analyses the criteria for a win/draw of his team depending on the…
A Football Association coach analyses the criteria for a win/draw of his team depending on the following conditions.
• If the Centre and Forward players perform well but Defenders do not perform well.
OR
• If Goalkeeper and Defenders perform well but the Centre players do not perform well.
OR
• If all perform well.
The inputs are:
(In all the above cases, 1 indicates yes and 0 indicates no.)
Output: X - Denotes the win/draw criteria [1 indicates win/draw and 0 indicates defeat in all cases]
Draw the truth table for the inputs and outputs given above and write the SOP expression for $X(C, D, F, G)$.
| INPUTS | |
|---|---|
| C | Centre players perform well |
| D | Defenders perform well |
| F | Forward players perform well |
| G | Goalkeeper perform well |
Answer
Answer
AITruth table for $X(C,D,F,G)$:
From the three given conditions:
Condition 1 (Centre, Forward well; Defenders not well): $C \cdot D' \cdot F$
Condition 2 (Goalkeeper, Defenders well; Centre not well): $C' \cdot D \cdot G$
Condition 3 (all perform well): $C \cdot D \cdot F \cdot G$
SOP expression: $X(C,D,F,G) = C \cdot D' \cdot F + C' \cdot D \cdot G + C \cdot D \cdot F \cdot G$
| C | D | F | G | 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 | 1 |
| 0 | 1 | 1 | 0 | 0 |
| 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 | 0 |
| 1 | 1 | 1 | 1 | 1 |
From ISC 2024 Specimen Computer Science Paper 1, question 3(i).