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Solution

Once the Karnaugh map has been constructed and the adjacent 1s linked by rectangular and square boxes, the algebraic minterms can be found by examining which variables stay the same within each box.

For the red grouping:

Thus the first minterm in the Boolean sum-of-products expression is A C.

For the green grouping, A and B maintain the same state, while C and D change. B is 0 and has to be negated before it can be included. The second term is therefore A B. Note that it is acceptable that the green grouping overlaps with the red one.

In the same way, the blue grouping gives the term BC D.

The solutions of each grouping are combined: the normal form of the circuit is A C ¯ + A B ¯ + B C D ¯ {\displaystyle A{\overline {C}}+A{\overline {B}}+BC{\overline {D}}}.

Thus the Karnaugh map has guided a simplification of

It would also have been possible to derive this simplification by carefully applying the axioms of Boolean algebra, but the time it takes to do that grows exponentially with the number of terms.