1
GATE ECE 2017 Set 1
+2
-0.6
Which one of the following gives the simplified sum of products expression for the Boolean function $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ where $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?
A
$$\overline A B + \,\overline A \,\overline B \,\overline C + \,A\overline B \,C$$
B
$$\overline A \,\overline C + \overline A B + A\overline B C$$
C
$$\overline A \,\overline C + A\,\overline B + A\overline B C$$
D
$$\overline A \,BC + \overline A \,\overline C + A\,\overline B C$$
2
GATE ECE 2016 Set 3
+2
-0.6
Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is
A
$$\overline P \,\overline {Q\,} \,S\overline X + P\overline Q \,S\overline X + Q\,\overline R \,\,\overline S X + QR\overline {S\,} X$$
B
$$\overline {Q\,} \,S\,\overline X \, + Q\,\overline S \,X$$
C
$$\overline {Q\,} S\,X + Q\,\overline S \,\overline X$$
D
$$\overline {Q\,} S\, + Q\,\overline S \,$$
3
GATE ECE 2015 Set 2
+2
-0.6
A function of Boolean variables X,Y and Z is expressed in terms of the min-terms as F(X, Y, Z)=$$\sum\limits_{}^{} {}$$m(1,2,5,6,7) Which one of the product of sums given below is equal to the funtion F(X, Y, Z)?
A
$$(\overline X + \overline Y + \overline Z ).(\overline X + Y + Z).(X + \overline Y + \overline Z )$$
B
$$(X + Y + Z).(X + \overline Y + \overline Z ).(\overline X + Y + Z)$$
C
$$(\overline X + \overline Y + Z).(\overline X + Y + \overline Z ).(X + \overline Y + Z).(X + Y + \overline Z ).(X + Y + Z)$$
D
$$(X + Y + \overline Z ).(\overline X + Y + Z).(\overline X + Y + \overline Z ).((\overline X + \overline Y + Z).(\overline X + \overline Y + \overline Z )$$
4
GATE ECE 2015 Set 1
+2
-0.6
The Boolean expression F(X, Y, Z)= $$\overline X Y\overline Z + X\overline {Y\,} \overline Z + XY\overline Z + XYZ$$ converted into the canonical product of sum (POS)from is
A
$$(x + y + z)(x + y + \overline z )(x + \overline y + \overline z )(\overline x + y + \overline z )$$
B
$$(x + \overline y + z)(\overline x + y + \overline z )(\overline x + \overline y + z)(\overline x + \overline y + z)$$
C
$$(x + y + z)(\overline x + y + \overline z )(x + \overline y + z)(\overline x + \overline y + \overline z )$$
D
$$(x + \overline y + \overline z )(\overline x + y + z)(\overline x + \overline y + z)(x + y + z)$$
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