Simplify the expression by using karnaugh map, Computer Engineering

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Simplify the following expression into sum of products using Karnaugh map

F(A, B, C, D) = ∑ (1,3,4,5,6,7,9,12,13)

Ans. Simplification of the given expression in sum of products using Karnaugh Map is shown below:

F(A,B,C,D) = Σ (1,3,4,5,6,7,9,12,13)

Karnaugh Map for F(A,B,C,D) = Σ (1,3,4,5,6,7,9,12,13) is demonstrated in figure (a). In this figure the grouping of cells is also shown.

819_Simplify the expression into sum of products using Karnaugh map.png

So the equations for (1) is A‾ B; and for (2) is C‾ D; for (3) is A‾ D; for (4) is B C‾

Thus, the Simplified Expression for the Karnaugh map as
F(A,B,C,D) = A‾ B+ C‾ D+ A‾ D+B C‾
= A‾ (B + D) + C‾ ( B + D)

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