1
GATE CSE 1997
+2
-0.6
Let $$f\left( {x,y,z} \right) = \overline x + \overline y x + xz$$ be a switching function. Which one of the following is valid?
A
$$\overline y x$$ is a prime implicates of $$f$$
B
$$xz$$ is a minters of $$f$$
C
$$xz$$ is an implicant of $$f$$
D
y is a prime applicant of $$f$$
2
GATE CSE 1997
+2
-0.6
Consider the logic circuit shown in Figure below. The functions $${f_1},$$ $${f_2}$$ and $$f$$ (in canonical sum of products form in decimal notation) are:

$${f_1}\left( {w,\,x,\,y,\,z} \right) = \sum {8,9,10}$$
$${f_2}\left( {w,\,x,\,y,\,z} \right) = \sum {7,8,12,13,18,15}$$
$$f\left( {w,\,x,\,y,\,z} \right) = \sum {\left( {8,9} \right)}$$

The function $${f_3}$$ is

A
$$\sum {9,\,10}$$
B
$$\sum 9$$
C
$$\sum {1,8,9}$$
D
$$\sum {8,10,15}$$
3
GATE CSE 1990
+2
-0.6
Two $$NAND$$ gates having open collector outputs are tied together as shown in fig. The logic function $$Y,$$ implemented by the circuit is.
A
$$Y = A\overline {BC} + \overline {DE}$$
B
$$Y = ABC + DE$$
C
$$Y = \overline {ABC} .\overline {DE}$$
D
$$Y = ABC\,.\,DE$$
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