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Reduce the Boolean function by using 4-variable Karnaugh map, showing the various groups (i.e…
(a)[4.0]
Reduce the Boolean function $F(A,B,C,D) = \pi (0, 1, 2, 3, 4, 6, 9, 11, 13)$ 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$F(A,B,C,D)=\pi(0,1,2,3,4,6,9,11,13)$ is in POS form, so the maxterms (0's) are plotted on a 4-variable K-map (rows AB: 00,01,11,10; columns CD: 00,01,11,10) and grouped:
Quad: maxterms $(0,2,4,6)$: common to all is $A=0, D=0 \Rightarrow (A+D)$
Quad: maxterms $(1,3,9,11)$: common to all is $B=0, D=1 \Rightarrow (B+D')$
Pair: maxterms $(9,13)$: common to both is $A=1,C=0,D=1 \Rightarrow (A'+C+D')$
Reduced POS expression: $F(A,B,C,D) = (A+D) \cdot (B+D') \cdot (A'+C+D')$
From ISC 2024 Specimen Computer Science Paper 1, question 4(i).