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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 $F(P, Q, R, S) = \Sigma (0,1,2,5,7,8,9,10,13,15)$ by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).
(b)[1.0]
Draw the logic gate diagram using NAND gates only for the reduced expression. Assume that the variables and their complements are available as inputs.
Draw: logic gate diagram
Answer
Answer (a)
AIK-map for $F(P,Q,R,S) = \Sigma(0,1,2,5,7,8,9,10,13,15)$:
- Quad ($m5,m7,m13,m15$): Q=1, S=1 -> term $QS$
- Quad ($m0,m1,m8,m9$): Q=0, R=0 -> term $Q'R'$
- Quad ($m0,m2,m8,m10$): Q=0, S=0 -> term $Q'S'$
Reduced (minimal) SOP expression: $F(P,Q,R,S) = QS + Q'R' + Q'S'$
From ISC 2025 Computer Science Paper 1, question 4(i).