870 views

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. $\sum 8, 10, 15$

edited | 870 views
0
Great explanations

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

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, $f_3 = \Sigma 9$
selected
–1 vote