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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 $F(A, B, C, D) = \Sigma(0, 1, 2, 4, 8, 9, 10, 12)$ 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.
Draw: logic gate diagram for the reduced expression
Answer
Answer (a)
AI$F(A,B,C,D) = \Sigma(0,1,2,4,8,9,10,12)$
Plotting the minterms on a 4-variable K-map (rows AB: 00,01,11,10; columns CD: 00,01,11,10):
- Quad 1: cells (0,1,8,9) — rows AB=00 & 10, columns CD=00 & 01 — C=0 and B=0 remain fixed while A and D vary → term reduces to $B'C'$
- Quad 2: cells (0,2,8,10) — B=0 and D=0 remain fixed while A and C vary → term reduces to $B'D'$
- Quad 3: cells (0,4,8,12) — C=0 and D=0 remain fixed while A and B vary → term reduces to $C'D'$
(All three quads are valid 4-cell groupings; cells 0 and 8 are shared between all three groups, which is allowed.)
Reduced (minimal) SOP:
$F(A,B,C,D) = B'C' + B'D' + C'D'$
From ISC 2026 Improvement Computer Science Paper 1, question 5(i).