‹ Back to the paper
A family intends to purchase a smart phone depending on the criteria given below: • Quad core…
A family intends to purchase a smart phone depending on the criteria given below:
• Quad core processor with internal memory of 64 GB or more but not a resale phone
OR
• Resale phone with quad core processor but without warranty
OR
• Processor is not a quad core but with a warranty of 1 year and the internal memory is of 64 GB or more
The inputs are:
(In all the above cases, 1 indicates yes and 0 indicates no.)
Output: X [1 indicates purchased, 0 indicates not purchased for all cases]
Draw the truth table for the inputs and outputs given above and write the SOP expression
| INPUTS | |
|---|---|
| P | Quad core processor |
| M | Internal memory of 64 GB or more |
| R | Resale phone |
| W | Warranty of 1 year |
Answer
Answer
AIInputs: P (quad core), M (memory >=64GB), R (resale), W (warranty of 1 year). Output X=1 when purchased.
Condition 1: $P \cdot M \cdot R'$ (quad core, memory>=64GB, not resale)
Condition 2: $R \cdot P \cdot W'$ (resale, quad core, no warranty)
Condition 3: $P' \cdot W \cdot M$ (not quad core, warranty of 1 yr, memory>=64GB)
Truth table (verified with the boolean tool):
SOP expression: $X = PMR' + PRW' + P'MW$
| P | M | R | W | 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 | 0 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 0 |
From ISC 2023 Specimen Computer Science Paper 1, question 4(i).