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Given the Boolean function: . Reduce the above expression by using 4-variable Karnaugh map, showing…
Given the Boolean function: $F(P, Q, R, S) = \pi ( 0, 1, 2, 8, 9, 11, 13, 15 )$.
(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 using only NOR gates. Assume that the variables and their complements are available as inputs.
Answer
Answer (i)
AIK-map for $F(P,Q,R,S)=\pi(0,1,2,8,9,11,13,15)$, grouping the 0s/maxterms (verified with the boolean/K-map tool):
Quad ($M_9,M_{11},M_{13},M_{15}$): P=1, S=1 $\to$ term $(P'+S')$
Pair ($M_0,M_2$): P=0, Q=0, S=0 $\to$ term $(P+Q+S)$
Quad ($M_0,M_1,M_8,M_9$): Q=0, R=0 $\to$ term $(Q+R)$
Reduced (minimal) POS expression: $F(P,Q,R,S) = (P'+S').(P+Q+S).(Q+R)$
From ISC 2019 Computer Science Paper 1, question 4(b).