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Consider a logic circuit shown in figure below. The functions $f_1, f_2 \text{ and } f$ (in canonical sum of products form in decimal notation) are :

$f_1 (w, x, y, z) = \sum 8, 9, 10$

$f_2 (w, x, y, z) = \sum 7, 8, 12, 13, 14, 15$

$f (w, x, y, z) = \sum 8, 9$

The function $f_3$ is

  1. $\sum 9, 10$
  2. $\sum 9$

  3. $\sum 1, 8, 9$

  4. $\sum 8, 10, 15$

asked in Digital Logic by Veteran (59.6k points)
edited by | 960 views
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2 Answers

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$f = (f_1 \wedge f_2) \vee f_3$

Since $f_1$ and $f_2$ are in canonical sum of products form, $f_1 \wedge  f_2$ will only contain their common terms- that is $f_1 \wedge f_2 = \Sigma 8$

Now, $\Sigma 8 \vee f_3 = \Sigma 8,9$
So, $f_3 = \Sigma 9$
answered by Veteran (363k points)
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