1
GATE CSE 2000
MCQ (Single Correct Answer)
+2
-0.6
The simultaneous equations on the Boolean variables $$x, y, z$$ and $$w,$$ $$x+y+z=1$$$$$xy=0$$$ $$xz+w=1$$$$$xy + \overline z \overline w = 0$$$
have the following for $$x, y, z$$ and $$w,$$ respectively.
A
$$0100$$
B
$$1101$$
C
$$1011$$
D
$$1000$$
2
GATE CSE 1999
MCQ (More than One Correct Answer)
+2
-0.6
Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function?
A
$$XOR$$ gates, $$NOT$$ gates
B
$$2$$ to $$1$$ multiplexers
C
$$AND$$ gates, $$XOR$$ gates
D
Three-input gates that output $$(A.B) + C$$ for the inputs $$A. B$$ and $$C.$$
3
GATE CSE 1997
MCQ (Single Correct Answer)
+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 $$f$$
4
GATE CSE 1997
MCQ (Single Correct Answer)
+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
$$\sum {8,10,15}$$
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