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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 $F(A, B, C, D) = \pi(0, 2, 4, 6, 8, 9, 10, 11, 14)$ 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(A,B,C,D) = π(0,2,4,6,8,9,10,11,14) is given in POS form, so the maxterms (0s) are plotted on a 4-variable K-map (rows AB: 00,01,11,10; columns CD: 00,01,11,10 - Gray code order) and grouped:
Group 1 (Quad): maxterms 8,9,10,11 (row A=1,B=0, all columns) -> term (A'+B)
Group 2 (Quad): maxterms 0,2,4,6 (columns CD=00,10 in rows AB=00,01) -> term (A+D)
Group 3 (Quad): maxterms 2,6,10,14 (column CD=10, all rows) -> term (C'+D)
Reduced (minimal) POS expression:
F(A,B,C,D) = (A'+B).(A+D).(C'+D)
From ISC 2024 Computer Science Paper 1, question 4(i).