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Given the Boolean function . Reduce the above expression by using 4-variable Karnaugh map, showing…
Given the Boolean function $F(A,B,C,D) = \pi(0, 1, 2, 4, 5, 8, 10, 11, 14, 15)$.
(a)[4.0]
Reduce the above expression 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)
AI$F(A,B,C,D) = \pi(0, 1, 2, 4, 5, 8, 10, 11, 14, 15)$. Plotting the 0s on a 4-variable K-map (rows AB, columns CD in the order 00, 01, 11, 10):
Groups (of 0s):
Quad 1 $\{M_0, M_1, M_4, M_5\}$: $(A + C)$
Quad 2 $\{M_{10}, M_{11}, M_{14}, M_{15}\}$: $(A' + C')$
Quad 3 (four corners) $\{M_0, M_2, M_8, M_{10}\}$: $(B + D)$
Reduced expression: $F = (A + C) \cdot (A' + C') \cdot (B + D)$
| AB \ CD | 00 | 01 | 11 | 10 |
| 00 | 0 | 0 | 1 | 0 |
| 01 | 0 | 0 | 1 | 1 |
| 11 | 1 | 1 | 0 | 0 |
| 10 | 0 | 1 | 0 | 0 |
From ISC 2023 Computer Science Paper 1, question 3(ii).