Digital Logic

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      Boolean Algebra
Question 2
If the numerical value of a 2-byte unsigned integer on a little endian computer is 255 more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer?
[MSQ]
A
0x6665
B
0x0001
C
0x4243
D
0x0100
GATE CSE 2021 SET-2      Number System
Question 3
If x and y are two decimal digits and (0.1101)_2 = (0.8xy5)_{10}, the decimal value of x+y is ___________
A
3
B
6
C
8
D
4
GATE CSE 2021 SET-2      Number System
Question 4
Which one of the following circuits implements the Boolean function given below?

f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6

where m_i is the i^{th} minterm.

A
A
B
B
C
C
D
D
GATE CSE 2021 SET-2      Combinational Circuit
Question 5
The format of the single-precision floating point representation of a real number as per the IEEE 754 standard is as follows:

\begin{array}{|c|c|c|} \hline \text{sign} & \text{exponent} & \text{mantissa} \\ \hline \end{array}

Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
A
exponent = 00000000 and mantissa = 0000000000000000000000000
B
exponent = 00000000 and mantissa = 0000000000000000000000001
C
exponent = 00000001 and mantissa = 0000000000000000000000000
D
exponent = 00000001 and mantissa = 0000000000000000000000001
GATE CSE 2021 SET-2      Number System
Question 6
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      Boolean Algebra
Question 7
Consider a 3-bit counter, designed using T flip-flops, as shown below:

Assuming the initial state of the counter given by PQR as 000, what are the next three states?
A
011,101,000
B
001,010,111
C
011,101,111
D
001,010,000
GATE CSE 2021 SET-1      Sequential Circuit
Question 8
Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S:1
E:10000001
F:11110000000000000000000

Here, S,E and F denote the sign, exponent, and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ____________.
A
-7.75
B
7.75
C
-3.825
D
3.825
GATE CSE 2021 SET-1      Number System
Question 9
Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?
A
15
B
21
C
D2
D
528
GATE CSE 2021 SET-1      Number System
Question 10
A new flipflop with inputs X and Y, has the following property
\begin{array}{|c|c|c|c|} \hline \mathbf{X} & \mathbf{Y} & \text { Current state } & \text { Next state } \\ \hline 0 & 0 & Q & 1 \\ 0 & 1 & Q & \bar{Q} \\ 1 & 1 & Q & 0 \\ 1 & 0 & Q & Q \\ \hline \end{array}
Which of the following expresses the next state in terms of X,Y, current state?
A
(\bar{X} \wedge \bar{Q}) \vee(\bar{Y} \wedge Q)
B
(\bar{X} \wedge {Q}) \vee(\bar{Y} \wedge \bar{Q})
C
({X} \wedge \bar{Q}) \vee({Y} \wedge {Q})
D
({X} \wedge \bar{Q}) \vee(\bar{Y} \wedge {Q})
ISRO CSE 2020      Sequential Circuit


There are 10 questions to complete.

9 thoughts on “Digital Logic”

Leave a Comment

Like this FREE website? Please share it among all your friends and join the campaign of FREE Education to ALL.