Question

Four large tanks at a chemical plant contain different liquids being heated. Liquid-level sensors are being used to detect whenever the level in tank A or tank B rises above a predetermined level. Temperature sensors in tank C and D detect when the temperature in either of these tanks drops below a prescribed temperature limit. Assume that the liquid-level sensor outputs A and B are LOW when the level is satisfactory and HIGH when the level is too high. Also, the temperaturesensor outputs C and D are LOW when the temperature is satisfactory and HIGH when the temperature is too low. Use K mapping and take advantage of the don't-care conditions. (i) Produce the truth table to verify the logic to detect whenever the level in tankA or tank B is too high at the same time that the temperature in either tankC or tankD is too low.

Answer 1

The student is looking to create a truth table for a detection system in a chemical plant, utilizing sensor outputs from four tanks. This truth table, along with Karnaugh mapping and 'don't care' conditions, will be used to design the logic circuit detecting high levels and low temperatures.

Step-by-step explanation:

The student's question involves the creation of a truth table for a detection system in a chemical plant. To detect an undesirable condition (either a high level in tanks A or B, or a low temperature in tanks C or D), we need to consider the different sensor outputs. Each sensor outputs a LOW signal when conditions are nominal and a HIGH signal when they are not. The truth table will help in developing a logic circuit using Karnaugh mapping (K mapping) by considering the various combinations of sensor outputs. Furthermore, 'don't care' conditions can be utilized as they represent scenarios that will not affect the final outcome and can simplify the logic circuit.

Here's a basic representation of how the truth table is constructed:

• Each tank has two possible states, represented by 0 (LOW) and 1 (HIGH).
• The output logic needs to be HIGH when Tank A or Tank B is HIGH AND simultaneously when Tank C or Tank D is HIGH.
• 'Don't care' conditions occur where the combination of tank states does not impact the detection system and can be noted as 'X' in the truth table.
• The Karnaugh map can then be used to simplify the resulting logic function based on the truth table.

This truth table and subsequent K mapping will aid in designing an efficient logic circuit for the system.