Digital Logic

Question 1
Consider three floating point numbers A, B and C stored in registers R_A, R_B and R_C, respectively as per IEEE-754 single precision floating point format. The 32-bit content stored in these registers (in hexadecimal form) are as follows.

R_A=0xC1400000
R_B=0x42100000
R_C=0x41400000

Which one of the following is FALSE?
A
A+C=0
B
C=A+B
C
B=3C
D
(B-C) \gt 0
GATE CSE 2022      Number System
Question 2
Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?
A
R1 = 1011 and R2 = 1110
B
R1 = 1100 and R2 = 1010
C
R1 = 0011 and R2 = 0100
D
R1 = 1001 and R2 = 1111
GATE CSE 2022      Number System
Question 3
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 4
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 5
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 6
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 7
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 8
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 9
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 10
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


There are 10 questions to complete.

12 thoughts on “Digital Logic”

  6. Question number 42 in the Digital Logic subject is not part of Boolean Algebra, it should be present in the propositional logic section on Discrete Mathematics.

    Reply

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