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Given the Boolean function . Reduce the above expression by using 4-variable Karnaugh map, showing…
Given the Boolean function $F(A, B, C, D) = \Sigma (0,2,4,8,9,10,12,13)$.
(i)[4.0]
Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).
(ii)[1.0]
Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.
Answer
Answer (i)
AI$F(A,B,C,D)=\Sigma(0,2,4,8,9,10,12,13)$. Plotting on a 4-variable K-map and grouping (verified with the boolean tool):
Quad {8,9,12,13}: $AC'$
Quad {0,2,8,10}: $B'D'$
Quad {0,4,8,12}: $C'D'$
Minimal SOP: $F = AC' + B'D' + C'D'$
From ISC 2018 Computer Science Paper 1, question 4(a).