A chemical plants needs a micro-processor driven alarm system to warm of critical conditions in one of its chemical tanks. The tank has 4 High/Low (1/0) switches that monitors temperature (T), pressure (P), fluid level (L) and weigt (W). This system will notify the microprocessor to activate alarm when following conditions occurs.
1. High fluid level with high temperature and high pressure.
2. Low fluid level with high temperature and high weight.
3. Low fluid level with high low temperature and high pressure.
4. Low fluid level with high temperature and low weight.
Which of these given option(s) is/are correct for activating the alarm?

$L T P W + L T P + ¯ ¯¯ ¯ L T W + ¯ ¯¯ ¯ L ¯ ¯¯ ¯ T P + ¯ ¯¯ ¯ L ¯ ¯¯¯¯ ¯ W T$

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$¯ ¯¯ ¯ L ¯ ¯¯ ¯ T ¯ ¯¯ ¯ P W + L T P + ¯ ¯¯ ¯ L T W + ¯ ¯¯ ¯ L ¯ ¯¯ ¯ T P + ¯ ¯¯ ¯ L ¯ ¯¯¯¯ ¯ W T$

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$L T P + ¯ ¯¯ ¯ L T W + ¯ ¯¯ ¯ L ¯ ¯¯ ¯ T P + ¯ ¯¯ ¯ L ¯ ¯¯¯¯ ¯ W T$

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T P + P ¯ ¯¯ ¯ L + T ¯ ¯¯ ¯ L

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Solution

The correct option is D $T P + P ¯ ¯¯ ¯ L + T ¯ ¯¯ ¯ L$
Alarm $= L T P + ¯ ¯¯ ¯ L T W + ¯ ¯¯ ¯ L ¯ ¯¯ ¯ T P + ¯ ¯¯ ¯ L ¯ ¯¯¯¯ ¯ W T$

$\Rightarrow$ For option (a) $= L T P (1 + W) + ¯ ¯¯ ¯ L T W + ¯ ¯¯ ¯ L ¯ ¯¯ ¯ T P + ¯ ¯¯ ¯ L ¯ ¯¯¯¯ ¯ W T$

$\Rightarrow$ Simplified form of alarm = $L T P + ¯ ¯¯ ¯ L T W + ¯ ¯¯ ¯ L ¯ ¯¯ ¯ T P + ¯ ¯¯ ¯ L ¯ ¯¯¯¯ ¯ W T$

$= T P + P ¯ ¯¯ ¯ L + T ¯ ¯¯ ¯ L$ (Using k-map)

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