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Given the Boolean function . Reduce the above expression by using 4-variable Karnaugh map, showing…
Given the Boolean function $F(A, B, C, D) = \pi(0, 1, 3, 5, 6, 7, 9, 11, 13, 14, 15)$.
(a)[4.0]
Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).
(b)[1.0]
Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.
Answer
Answer (a)
AI$F(A,B,C,D)=\pi(0,1,3,5,6,7,9,11,13,14,15)$. Plotting the maxterms on a 4-variable K-map and grouping the 0's (verified with the boolean tool):
Pair {0,1}: $(A+B+C)$
Quad {6,7,14,15}: $(B'+C')$
Octet {1,3,5,7,9,11,13,15}: $D'$
Minimal POS: $F = (A+B+C)\cdot(B'+C')\cdot D'$
From ISC 2023 Specimen Computer Science Paper 1, question 3(ii).