For three variables A, B, C, which maxterm index corresponds to the expression A + B + C in canonical Product-of-Maxterms form?
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AM0
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BM1
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CM3
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DM4
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EM7
Answer
Correct Answer: M0
Explanation
Introduction / Context:Canonical Product-of-Maxterms (ΠM) expresses a logic function as the product (AND) of maxterms. Each maxterm corresponds to a specific input combination where the function is zero.
Given Data / Assumptions:
- Variables ordered as A (MSB), B, C (LSB).
- Maxterm notation Mi corresponds to the input combination i for which the maxterm evaluates to 0 and the function can be zero.
Concept / Approach:
Maxterm Mi is formed by ORing each variable in true or complemented form such that the term evaluates to 0 for the i-th input combination. For i = 0 → (A, B, C) = (0, 0, 0), the maxterm is A + B + C.
Step-by-Step Solution:
At input (0,0,0), to force the OR to 0, each literal must be 0 → use A, B, C uncomplemented.Thus the canonical maxterm is A + B + C, which by definition is M0.Verification / Alternative check:
Enumerate the 3-variable maxterms: M0 = A + B + C, M1 = A + B + C', etc. Standard tables confirm this mapping.
Why Other Options Are Wrong:
- M1, M3, M4: correspond to different input indices and therefore different literal complements.
- M7: corresponds to (1,1,1) and is A' + B' + C'.
Common Pitfalls:
Confusing minterms with maxterms, or mixing up literal complementation rules between SOP and POS canonical forms.
Final Answer:
M0