Reduce the Boolean function by using 4-variable Karnaugh map, showing the various groups (i.e…
(a)[4.0]
Reduce the Boolean function $F(A,B,C,D) = \pi (0,1,2,3,7,8,9,10,11,12,13,15)$ by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).
(b)[1.0]
Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.
Draw: logic gate diagram
Answer
Answer (a)
AIWritten by AI (antigravity) - it can contain mistakes.
Given function in POS form: F(A, B, C, D) = π(0, 1, 2, 3, 7, 8, 9, 10, 11, 12, 13, 15)
Plotting maxterms (0s) on a 4-variable Karnaugh map (rows AB: 00=A+B, 01=A+B', 11=A'+B', 10=A'+B; columns CD: 00=C+D, 01=C+D', 11=C'+D', 10=C'+D):
- Group 1 (Octet): cells (0, 1, 2, 3, 8, 9, 10, 11) formed by row 00 (A+B) and row 10 (A'+B) across all columns. A is eliminated, C and D are eliminated. Reduces to: B
- Group 2 (Quad): cells (8, 9, 12, 13) in rows 10, 11 and columns 00, 01. B is eliminated, D is eliminated. Reduces to: (A' + C)
- Group 3 (Quad): cells (3, 7, 11, 15) in column 11 across all four rows. AB are eliminated. Reduces to: (C' + D')
Reduced POS expression:
F(A, B, C, D) = B • (A' + C) • (C' + D')
From ISC 2026 Computer Science Paper 1, question 5(i).