Five-variable K-maps: Which statement correctly describes the structure/usage of a 5-variable Karnaugh map?
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AThere is no such thing.
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BIt can be used only with a computer.
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CIt is made up of two 4-variable Karnaugh maps.
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DIt is made up of a 2-variable and a 3-variable Karnaugh map.
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EIt must be drawn as a single 32-cell grid without partitioning.
Answer
Correct Answer: It is made up of two 4-variable Karnaugh maps.
Explanation
Introduction / Context:K-maps extend beyond four variables. For five variables, a common hand technique uses two 4-variable maps, one for the fifth variable at 0 and one for it at 1, with grouping allowed across corresponding cells.
Given Data / Assumptions:
- We want a practical way to visualize 5-variable functions.
- Manual simplification methods are acceptable.
Concept / Approach:By splitting the fifth variable into two “layers,” each layer is a standard 4-variable map. Adjacent cells across the two layers are also eligible for grouping, enabling larger implicants and proper minimization.
Step-by-Step Solution:
Step 1: Create two 4-variable K-maps labeled V=0 and V=1 for the fifth variable V.Step 2: Plot minterms on the appropriate layer.Step 3: Group across layers when corresponding cells are both 1 to form larger implicants.Verification / Alternative check:Mapping back to algebra confirms valid implicants and correct simplification.
Why Other Options Are Wrong:
There is no such thing: 5-variable K-maps exist.Only with a computer: Manual two-layer method is standard.2-var + 3-var composition: Not how 5-var K-maps are constructed.Single 32-cell grid only: Two-layer approach is common and equivalent.Common Pitfalls:Forgetting cross-layer adjacency, which prevents achieving maximal groups.
Final Answer:It is made up of two 4-variable Karnaugh maps.