Boolean Algebra

Question 1
Consider a Boolean function f(w,x,y,z) such that

\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}

The number of literals in the minimal sum-of-products expression of f is ________
A
4
B
6
C
8
D
9
GATE CSE 2021 SET-2   Digital Logic
Question 2
Consider the following Boolean expression.

F=(X+Y+Z)(\overline X +Y)(\overline Y +Z)

Which of the following Boolean expressions is/are equivalent to \overline F (complement of F)?
[MSQ]
A
(\overline X +\overline Y +\overline Z)(X+\overline Y)(Y+\overline Z)
B
X\overline Y + \overline Z
C
(X+\overline Z)(\overline Y +\overline Z)
D
X\overline Y +Y\overline Z + \bar X \bar Y \bar Z
GATE CSE 2021 SET-1   Digital Logic
Question 3
The following circuit compares two 2-bit binary numbers, X and Y represented by X_{1}X_{0} and Y_{1}Y_{0} respectively. (X_{0} and Y_{0} represent Least Significant Bits)

Under what conditions Z will be 1?
A
X > Y
B
X < Y
C
X=Y
D
X!=Y
ISRO CSE 2020   Digital Logic
Question 4
If ABCD is a 4-bit binary number, then what is the code generated by the following circuit?

A
BCD code
B
Gray code
C
8421 code
D
Excess-3 code
ISRO CSE 2020   Digital Logic
Question 5
Minimum number of NAND gates required to implement the following binary equationY=(\bar{A}+\bar{B})(C+D)
A
4
B
5
C
3
D
6
ISRO CSE 2020   Digital Logic
Question 6
Consider the Boolean function z(a,b,c).

Which one of the following minterm lists represents the circuit given above?
A
z=\Sigma (0,1,3,7)
B
z=\Sigma (1,4,5,6,7)
C
z=\Sigma (2,4,5,6,7)
D
z=\Sigma (2,3,5)
GATE CSE 2020   Digital Logic
Question 7
What is the minimum number of 2-input NOR gates required to implement 4-variable function expressed in sum-of-minterms from as f = \Sigma (0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer ________ .
A
2
B
3
C
4
D
5
GATE CSE 2019   Digital Logic
Question 8
Consider three 4-variable functions f_1,f_2 \; and \; f_3, which are expressed in sum-of-minterms

f_1=\Sigma (0,2,5,8,14)
f_2=\Sigma (2,3,6,8,14,15)
f_3=\Sigma (2,7,11,14)

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:
A
\Sigma (7,8,11)
B
\Sigma (2,7,8,11,14)
C
\Sigma (2,14)
D
\Sigma (0,2,3,5,6,7,8,11,14,15)
GATE CSE 2019   Digital Logic
Question 9
Which one of the following is NOT a valid identity?
A
(x\oplus y)\oplus z=x\oplus (y\oplus z)
B
(x+ y)\oplus z=x\oplus (y+z)
C
x\oplus y=x+y, \; if \; xy=0
D
x\oplus y=(xy+x'y')'
GATE CSE 2019   Digital Logic
Question 10
Any set of Boolean operation that is sufficient to represent all Boolean expression is said to be complete. Which of the following is not complete ?
A
{AND, OR}
B
{AND, NOT}
C
{NOT, OR}
D
{NOR}
ISRO CSE 2018   Digital Logic


There are 10 questions to complete.

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