Karnaugh map (K-map) purpose: Confirm whether a K-map provides a graphical approach to minimizing (simplifying) Boolean sum-of-products expressions.

Difficulty: Easy

Correct Answer: Correct

Explanation:


Introduction / Context:
Karnaugh maps are a visual technique for simplifying Boolean expressions by grouping adjacent minterms to eliminate variables. They are widely taught as a stepping stone to Quine–McCluskey and modern synthesis tools.



Given Data / Assumptions:

  • We focus on minimizing sum-of-products (SOP) forms via minterm grouping.
  • Variables typically range from 2 to 4 (paper), but 5–6 are possible with care.
  • Adjacency is defined on Gray-coded map layouts.


Concept / Approach:
Each 1 cell on a K-map represents a minterm. Grouping 1s in powers of 2 (1, 2, 4, 8, …) removes changing variables from the product term, yielding simpler SOP expressions. K-maps also support POS by grouping 0s, but the statement’s focus on SOP is correct and common.



Step-by-Step Solution:

Plot minterms (1s) of the function on the map.Group adjacent 1s in largest possible power-of-two rectangles (wrapping edges is allowed).For each group, form the simplified product term by retaining only variables that do not change within the group.Sum (OR) the product terms to obtain the minimized SOP expression.


Verification / Alternative check:
Compare to algebraic simplification or to a logic minimizer; results match for canonical SOP minimization.



Why Other Options Are Wrong:

Incorrect: K-maps are indeed graphical simplifiers.Only POS: K-maps work for both SOP (group 1s) and POS (group 0s).Only for exactly 3 variables: Common from 2 to 4 variables; extensions exist for more.


Common Pitfalls:
Missing wrap-around adjacencies; making many small groups instead of fewer large ones; mixing SOP and POS grouping rules.


Final Answer:
Correct

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