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Given the Boolean function . Reduce the above expression by using 4-variable Karnaugh map, showing…
Given the Boolean function $F(A, B, C, D) = \Sigma ( 0, 2, 3, 4, 5, 8, 10, 11, 12, 13 )$.
(i)[4.0]
Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).
(ii)[1.0]
Draw the logic gate diagram for the reduced expression using only NAND gates. Assume that the variables and their complements are available as inputs.
Answer
Answer (i)
AIK-map for $F(A,B,C,D)=\Sigma(0,2,3,4,5,8,10,11,12,13)$ (verified with the boolean/K-map tool):
Quad ($m_4,m_5,m_{12},m_{13}$): B=1, C=0 $\to$ term $BC'$
Quad ($m_2,m_3,m_{10},m_{11}$): B=0, C=1 $\to$ term $B'C$
Quad ($m_0,m_4,m_8,m_{12}$): C=0, D=0 $\to$ term $C'D'$
Reduced (minimal) SOP expression: $F(A,B,C,D) = BC' + B'C + C'D'$
From ISC 2019 Computer Science Paper 1, question 4(a).