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Answer :
Final answer:
The student is inquiring about simplifying boolean expressions from ladder logic programs. All four expressions provided (L1 AND L2 AND L3, L1 OR L2 OR L3, L1 AND (L2 OR L3), L1 OR (L2 AND L3)) are already in their simplest form using Boolean algebra, assuming no additional information about the relationships between L1, L2, and L3 is given.
Explanation:
The student is asking for the initial Boolean expression for a given ladder logic program and how to simplify it. The options provided represent different logical operations that can be performed on inputs L1, L2, and L3. Ladder logic is primarily used in programmable logic controllers (PLCs) for industrial automation. To simplify the given expressions, we use Boolean algebra principles.
- For expression (a) L1 AND L2 AND L3, there is no simplification needed as it is already in its simplest form.
- For expression (b) L1 OR L2 OR L3, this is also already as simplified as it can be.
- For expression (c) L1 AND (L2 OR L3), there is no further simplification unless additional relationships between L2 and L3 are known.
- For expression (d) L1 OR (L2 AND L3), similar to the previous expressions, without additional information, this is the simplest form.
In conclusion, each Boolean expression given corresponds to a particular configuration of a ladder logic diagram and reflects different logic gate configurations. Without further context or relationships between the variables, these expressions are already in their simplest forms.
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