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Given the Boolean function . Reduce the above expression by using 4-variable Karnaugh map, showing…
Given the Boolean function $F(A, B, C, D) = \sum(0, 1, 2, 3, 4, 6, 9, 11, 13)$.
(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$F(A,B,C,D)=\Sigma(0,1,2,3,4,6,9,11,13)$. Plotting on a 4-variable K-map and grouping (verified with the boolean tool):
Quad {0,2,4,6}: $A'D'$
Quad {1,3,9,11}: $B'D$
Pair {9,13}: $AC'D$
Minimal SOP: $F = A'D' + B'D + AC'D$
From ISC 2023 Specimen Computer Science Paper 1, question 3(i).