GATE CS Boolean Algebra questions

Practise Boolean Algebra questions for GATE CS. Explore official PYQs and original topic-wise quizzes, check answers and view available solutions. Free, no sign-in.

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SubjectTopicYearType

Let

\oplus

denote the exclusive OR (XOR) operation. Let '

1

' and '

0

' denote the binary constants. Consider the following Boolean expression for

F

over two variables

P

and

Q

F(P,Q)=\left( \left(1 \oplus P \right) \oplus \left( P \oplus Q \right )\right ) \oplus \left(\left(P \oplus Q\right) \oplus \left(Q \oplus 0\right)\right)

The …

Which one of the following expressions does NOT represent exclusive NOR of

x

and

y

The truth table

{\begin{array}{|c|c|c|}\hline \textbf{X}& \textbf{Y}& \textbf{(X,Y)} \\ \hline 0& 0& 0 \\ \hline 0& 1&0\\ \hline 1& 0& 1 \\ \hline 1& 1& 1 \\ \hline \end{array}}

represents the Boolean function

The minterm expansion of

f(P,Q,R) = PQ +Q \bar{R}+P\bar{R}

P, Q, R

are Boolean variables, then

(P + \bar{Q}) (P.\bar{Q} + P.R) (\bar{P}.\bar{R} + \bar{Q})

simplifies to

Given

f_1

f_3

and

f

in canonical sum of products form (in decimal) for the circuit

f_1 = \Sigma m(4, 5, 6, 7, 8)

f_3 = \Sigma m(1, 6, 15)

f = \Sigma m(1, 6, 8, 15)

then

f_2

Which of the following is TRUE about formulae in Conjunctive Normal Form?

Define the connective

*

for the Boolean variables

X

and

Y

as:

X * Y = XY + X'Y'.

Let

Z = X * Y

. Consider the following expressions

P

Q

and

R

P : X = Y * Z, \\ Q :Y = X * Z, \\ R : X *Y * Z = 1

Which of the following is TRUE?

Let

f(w, x, y, z) = \sum {\left(0,4,5,7,8,9,13,15\right)}

. Which of the following expressions are NOT equivalent to

f

? P:

x'y'z' + w'xy' + wy'z + xz

w'y'z' + wx'y' + xz

w'y'z' + wx'y' + xyz+xy'z

x'y'z' + wx'y'+ w'y

A Boolean function

x’y’ + xy + x’y

is equivalent to

Let

f(A,B) = A'+B

. Simplified expression for function

f(f(x+y, y), z)

The simultaneous equations on the Boolean variables

x, y, z

and

w

x + y + z = 1

xy = 0

xz + w = 1

xy + \bar{z}\bar{w} = 0

have the following solution for

x, y, z

and

w,

respectively:

Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function?

Which of the following expressions is not equivalent to

\bar{x}

Which of the following operations is commutative but not associative?

What happens when a bit-string is XORed with itself

n

-times as shown:

\left[B \oplus (B \oplus ( B \oplus (B \dots n \text{ times}\right]

Let

*

be defined as

x * y = \bar{x} + y

. Let

z = x * y

. Value of

z * x

What values of

A, B, C

and

D

satisfy the following simultaneous Boolean equations?

\overline{A} + AB =0, AB=AC, AB+A\overline{C}+CD=\overline{C}D

The operation which is commutative but not associative is:

The Boolean expression

A \oplus B \oplus A

is equivalent to