The Boolean function with the Karnaugh map is :

2017

The Boolean function with the Karnaugh map

is :

  1. A.

    (A+C).D+B

  2. B.

    (A+B).C+D

  3. C.

    (A+D).C+B

  4. D.

    (A+C).B+D

Attempted by 179 students.

Show answer & explanation

Correct answer: A

Solution:

  • Group the two middle columns (AB = 01 and AB = 11). These columns are all ones, giving the term B.

  • Group the entire row where C = 1 and D = 1 (CD = 11). This gives the term C·D.

  • The remaining uncovered 1s require A·D (these occur when A = 1 and D = 1 while B = 0 and C = 0).

Combine the terms: B + C·D + A·D.

Factor D from the last two terms:

B + D·(A + C)

Final simplified expression: (A + C)·D + B.

This matches the given Karnaugh map and is a minimal form obtained by grouping columns and the CD row, then covering remaining 1s.

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