GATE ECE 2015 Set 2 | Boolean Algebra Question 6 | Digital Circuits

GATE ECE 2015 Set 2

MCQ (Single Correct Answer)

-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)?

$$(\overline X + \overline Y + \overline Z ).(\overline X + Y + Z).(X + \overline Y + \overline Z )$$

$$(X + Y + Z).(X + \overline Y + \overline Z ).(\overline X + Y + Z)$$

$$(\overline X + \overline Y + Z).(\overline X + Y + \overline Z ).(X + \overline Y + Z).(X + Y + \overline Z ).(X + Y + Z)$$

$$(X + Y + \overline Z ).(\overline X + Y + Z).(\overline X + Y + \overline Z ).((\overline X + \overline Y + Z).(\overline X + \overline Y + \overline Z )$$

GATE ECE 2015 Set 1

MCQ (Single Correct Answer)

-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

$$(x + y + z)(x + y + \overline z )(x + \overline y + \overline z )(\overline x + y + \overline z )$$

$$(x + \overline y + z)(\overline x + y + \overline z )(\overline x + \overline y + z)(\overline x + \overline y + z)$$

$$(x + y + z)(\overline x + y + \overline z )(x + \overline y + z)(\overline x + \overline y + \overline z )$$

$$(x + \overline y + \overline z )(\overline x + y + z)(\overline x + \overline y + z)(x + y + z)$$

GATE ECE 2014 Set 1

MCQ (Single Correct Answer)

-0.6

Consider the Boolean function, F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline {x\,} \,\overline y \,$$ $$\overline z $$ Which one of the following is the complete set of essential prime implicants?

$$w,y,xz,\overline x \,\overline z $$

w, y, xz

$$y,\overline x \,\overline {y\,} \overline {\,z} $$

y, xz, $$\overline x \,\,\overline {\,z} $$

GATE ECE 2009

MCQ (Single Correct Answer)

-0.6

If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$$ $$\left\{ {\overline X + \overline Z (X + Y)} \right\} = 1,$$ then

Y=Z

Y= $${\overline Z }$$

Z= 1

Z= 0

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