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Given the Boolean function . Reduce the above expression by using 4-variable Karnaugh map, showing…
Given the Boolean function $F(A,B,C,D) = \Sigma(2, 3, 6, 7, 8, 10, 12, 14, 15)$.
(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$F(A,B,C,D) = \Sigma(2, 3, 6, 7, 8, 10, 12, 14, 15)$. Plotting the 1s on a 4-variable K-map (rows AB, columns CD in the order 00, 01, 11, 10):
Groups:
Quad 1 $\{m_2, m_3, m_6, m_7\}$: $A'C$
Quad 2 $\{m_6, m_7, m_{14}, m_{15}\}$: $BC$
Quad 3 $\{m_8, m_{10}, m_{12}, m_{14}\}$: $AD'$
Reduced expression: $F = A'C + BC + AD'$
| AB \ CD | 00 | 01 | 11 | 10 |
| 00 | 0 | 0 | 1 | 1 |
| 01 | 0 | 0 | 1 | 1 |
| 11 | 1 | 0 | 1 | 1 |
| 10 | 1 | 0 | 0 | 1 |
From ISC 2023 Computer Science Paper 1, question 3(i).