‹ Back to the paper
Reduce the Boolean function by using 4-variable Karnaugh map, showing the various groups (i.e…
(a)[4.0]
Reduce the Boolean function $F(X, Y, Z, W) = \pi(0, 1, 2, 3, 4, 6, 8, 9, 11, 12)$ 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)
AIF(X,Y,Z,W) = π(0,1,2,3,4,6,8,9,11,12) is in POS form, so plot the maxterms (0's) on a 4-variable K-map (rows XY: 00,01,11,10; columns ZW: 00,01,11,10) and group them:
Group 1 (Quad): maxterms 0,2,4,6 → term (X + W)
Group 2 (Quad): maxterms 1,3,9,11 → term (Y + W')
Group 3 (Quad): maxterms 0,4,8,12 → term (Z + W)
Reduced POS expression: F(X,Y,Z,W) = (X + W).(Y + W').(Z + W)
From ISC 2025 Improvement Computer Science Paper 1, question 4(i).