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An automated parking gate uses four binary sensors. The parking gate should open under any one of…
An automated parking gate uses four binary sensors. The parking gate should open under any one of the following conditions:
- Vehicle detected and parking slot available
OR
- Parking slot available and either payment confirmed or VIP access granted
OR
- Payment not confirmed but VIP access granted
The inputs are:
(In all the above cases, 1 indicates YES and 0 indicates NO)
Output: X - Denotes opening of the parking gate (1 = Open, 0 = Close)
Draw the truth table for the inputs and outputs given above. Write the SOP expression for $X(V, S, P, I)$.
| INPUTS | |
|---|---|
| V | Vehicle detected |
| S | Parking slot available |
| P | Payment confirmed |
| I | VIP access granted |
Answer
Answer
AI$X(V,S,P,I) = V\cdot S \;+\; S\cdot(P+I) \;+\; P'\cdot I$
Truth Table:
SOP expression (from the given conditions):
$X = V\cdot S + S\cdot P + S\cdot I + P'\cdot I$
(This reduces, by K-map, to the minimal SOP $X = I\cdot P' + P\cdot S + S\cdot V$, since the term $S\cdot I$ is a redundant consensus term.)
| V | S | P | I | X |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 |
From ISC 2026 Improvement Computer Science Paper 1, question 4(i).