Search results for digital / GATE Overflow for GATE CSE

54 votes

5 answers

41

GATE CSE 2003 | Question: 44
A $\text{1-input}$, $\text{2-output}$ synchronous sequential circuit behaves as follows: Let $z_k, n_k$ denote the number of $0's$ and $1's$ respectively in initial $k$ bits of the input $(z_k+n_k=k)$. The circuit outputs $00$ until one of the ... is $01$. What is the minimum number of states required in the state transition graph of the above circuit? $5$ $6$ $7$ $8$

A $\text{1-input}$, $\text{2-output}$ synchronous sequential circuit behaves as follows:Let $z_k, n_k$ denote the number of $0’s$ and $1’s$ respectively in initial $k...

Kathleen

11.9k views

Kathleen asked Sep 17, 2014

27 votes

4 answers

42

GATE CSE 2020 | Question: 29
Consider three registers $R1$, $R2$, and $R3$ that store numbers in $\textsf{IEEE-754}$ single precision floating point format. Assume that $R1$ and $R2$ contain the values (in hexadecimal notation) $\textsf{0x42200000}$ ... what is the value stored in $R3$? $\textsf{0x40800000}$ $\textsf{0xC0800000}$ $\textsf{0x83400000}$ $\textsf{0xC8500000}$

Consider three registers $R1$, $R2$, and $R3$ that store numbers in $\textsf{IEEE-754}$ single precision floating point format. Assume that $R1$ and $R2$ contain the valu...

Arjun

18.5k views

Arjun asked Feb 12, 2020

35 votes

9 answers

43

GATE CSE 2019 | Question: 22
Two numbers are chosen independently and uniformly at random from the set $\{1,2,\ldots,13\}.$ The probability (rounded off to $3$ decimal places) that their $4\text{-bit}$ (unsigned) binary representations have the same most significant bit is ___________.

Two numbers are chosen independently and uniformly at random from the set $\{1,2,\ldots,13\}.$The probability (rounded off to $3$ decimal places) that their $4\text{-bit}...

Arjun

20.1k views

Arjun asked Feb 7, 2019

6 votes

2 answers

44

GATE CSE 2023 | Question: 22
A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is _____________.

A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is _____________.

admin

12.5k views

admin asked Feb 15, 2023

6 votes

1 answer

45

GATE CSE 2023 | Question: 33
Consider a sequential digital circuit consisting of $\mathrm{T}$ flip-flops and $\mathrm{D}$ flip-flops as shown in the figure. $\text{CLKIN}$ is the clock input to the circuit. At the beginning, $\text{Q1, Q2}$ and $\text{Q3}$ have values $0,1$ and $1,$ respectively. ... $\text{NEVER}$ be obtained with this digital circuit? $(0,0,1)$ $(1,0,0)$ $(1,0,1)$ $(1,1,1)$

Consider a sequential digital circuit consisting of $\mathrm{T}$ flip-flops and $\mathrm{D}$ flip-flops as shown in the figure. $\text{CLKIN}$ is the clock input to the c...

admin

9.0k views

admin asked Feb 15, 2023

30 votes

4 answers

46

GATE CSE 2001 | Question: 2.10
The $2's$ complement representation of (-539)10 in hexadecimal is $ABE$ $DBC$ $DE5$ $9E7$

The $2's$ complement representation of (-539)10 in hexadecimal is$ABE$$DBC$$DE5$$9E7$

Kathleen

12.1k views

Kathleen asked Sep 14, 2014

41 votes

4 answers

47

GATE CSE 2000 | Question: 2.14
Consider the values of $A = 2.0 \times 10^{30}, B = -2.0 \times 10^{30}, C = 1.0,$ and the sequence X:= A + B Y:= A + C X:= X + C Y:= Y + B executed on a computer where floating point numbers are represented with $32$ bits. The values for $X$ and $Y$ will be $X = 1.0, Y = 1.0$ $X = 1.0, Y = 0.0$ $X = 0.0, Y = 1.0$ $X = 0.0, Y = 0.0$

Consider the values of $A = 2.0 \times 10^{30}, B = -2.0 \times 10^{30}, C = 1.0,$ and the sequence X:= A + B Y:= A + C X:= X + C Y:= Y + Bexecuted on a computer where fl...

Kathleen

12.0k views

Kathleen asked Sep 14, 2014

3 votes

5 answers

48

GATE CSE 2024 | Set 1 | Question: 3
Consider a system that uses $5$ bits for representing signed integers in $2$ 's complement format. In this system, two integers $A$ and $B$ are represented as $A$=$01010$ and $B$=$11010$. Which one of the following operations will result in either an arithmetic overflow or an arithmetic underflow? $A+B$ $A-B$ $B-A$ $2 * B$

Consider a system that uses $5$ bits for representing signed integers in $2$ 's complement format. In this system, two integers $A$ and $B$ are represented as $A$=$01010$...

Arjun

3.8k views

Arjun asked Feb 16

57 votes

4 answers

49

GATE CSE 2002 | Question: 2-1
Consider the following logic circuit whose inputs are functions $f_1, f_2, f_3$ and output is $f$ Given that $f_1(x,y,z) = \Sigma (0,1,3,5)$ $f_2(x,y,z) = \Sigma (6,7),$ and $f(x,y,z) = \Sigma (1,4,5).$ $f_3$ is $\Sigma (1,4,5)$ $\Sigma (6,7)$ $\Sigma (0,1,3,5)$ None of the above

Consider the following logic circuit whose inputs are functions $f_1, f_2, f_3$ and output is $f$Given that$f_1(x,y,z) = \Sigma (0,1,3,5)$$f_2(x,y,z) = \Sigma (6,7),$ and...

Kathleen

14.5k views

Kathleen asked Sep 15, 2014

10 votes

6 answers

50

ISRO2015-8
Minimum number of $2 \times 1$ multiplexers required to realize the following function, $f = \overline{A} \;\overline{B} C + \overline{A}\; \overline{B} \;\overline{C}$ Assume that inputs are available only in true form and Boolean a constant $1$ and $0$ are available. $1$ $2$ $3$ $7$

Minimum number of $2 \times 1$ multiplexers required to realize the following function, $f = \overline{A} \;\overline{B} C + \overline{A}\; \overline{B} \;\overline{C}$As...

go_editor

10.7k views

go_editor asked Jun 16, 2016

36 votes

5 answers

51

GATE CSE 2015 Set 3 | Question: 35
Consider the equation $(43)_x = (y3)_8$ where $x$ and $y$ are unknown. The number of possible solutions is _____

Consider the equation $(43)_x = (y3)_8$ where $x$ and $y$ are unknown. The number of possible solutions is _____

go_editor

10.0k views

go_editor asked Feb 15, 2015

9 votes

5 answers

52

ISRO2007-04
When two numbers are added in excess-$3$ code and the sum is less than $9$, then in order to get the correct answer it is necessary to subtract $0011$ from the sum add $0011$ to the sum subtract $0110$ from the sum add $0110$ to the sum

When two numbers are added in excess-$3$ code and the sum is less than $9$, then in order to get the correct answer it is necessary tosubtract $0011$ from the sumadd $001...

go_editor

10.6k views

go_editor asked Jun 10, 2016

7 votes

3 answers

53

GATE CSE 2022 | Question: 31
Consider three floating point numbers $\textit{A, B}$ and $\textit{C}$ stored in registers $\text{R}_{\text{A}}, \text{R}_{\text{B}}$ and $\text{R}_{\text{C}},$ respectively as per $\textsf{IEEE-754}$ single precision floating point format. The $\text{32-bit}$ content stored in ... $\textit{A + C} = 0$ $\textit{C = A + B}$ $\textit{B =3C}$ $\textit{(B - C)} > 0$

Consider three floating point numbers $\textit{A, B}$ and $\textit{C}$ stored in registers $\text{R}_{\text{A}}, \text{R}_{\text{B}}$ and $\text{R}_{\text{C}},$ respectiv...

Arjun

8.6k views

Arjun asked Feb 15, 2022

1 votes

2 answers

54

GATE CSE 2024 | Set 2 | Question: 20
For a Boolean variable $x$, which of the following statements is/are FALSE? $x .1=x$ $x+1=x$ $x \cdot x=0$ $x+\bar{x}=1$

For a Boolean variable $x$, which of the following statements is/are FALSE?$x .1=x$$x+1=x$$x \cdot x=0$$x+\bar{x}=1$

Arjun

2.1k views

Arjun asked Feb 16

32 votes

7 answers

55

GATE CSE 2019 | Question: 30
Consider three $4$-variable functions $f_1, f_2$, and $f_3$, which are expressed in sum-of-minterms as $f_1=\Sigma(0,2,5,8,14),$ $f_2=\Sigma(2,3,6,8,14,15),$ $f_3=\Sigma (2,7,11,14)$ For the following circuit with one AND gate and one XOR gate the output function $f$ can be ... as: $\Sigma(7,8,11)$ $\Sigma (2,7,8,11,14)$ $\Sigma (2,14)$ $\Sigma (0,2,3,5,6,7,8,11,14,15)$

Consider three $4$-variable functions $f_1, f_2$, and $f_3$, which are expressed in sum-of-minterms as$f_1=\Sigma(0,2,5,8,14),$$f_2=\Sigma(2,3,6,8,14,15),$$f_3=\Sigma (2,...

Arjun

14.4k views

Arjun asked Feb 7, 2019

62 votes

5 answers

56

GATE CSE 2001 | Question: 2.8
Consider the following circuit with initial state $Q_0 = Q_1 = 0$. The D Flip-flops are positive edged triggered and have set up times 20 nanosecond and hold times $0.$ Consider the following timing diagrams of X and C. The clock period of $C \geq 40$ nanosecond. Which one is the correct plot of Y?

Consider the following circuit with initial state $Q_0 = Q_1 = 0$. The D Flip-flops are positive edged triggered and have set up times 20 nanosecond and hold times $0.$Co...

Kathleen

21.4k views

Kathleen asked Sep 14, 2014

3 votes

1 answer

57

GATE CSE 2024 | Set 2 | Question: 40
Consider $4$-variable functions $f 1, f 2, f 3, f 4$ expressed in sum-of-minterms form as given below. \[ \begin{array}{l} f 1=\sum(0,2,3,5,7,8,11,13) \\ f 2=\sum(1,3,5,7,11,13,15) \\ f 3=\sum(0,1,4,11) \\ f 4=\sum(0,2,6,13) \end{array} \] With ... $\boldsymbol{Y}=\sum(0,1,2,3,4,5,6,7)$ $\boldsymbol{Y}=\Pi(8,9,10,11,12,13,14,15)$

Consider $4$-variable functions $f 1, f 2, f 3, f 4$ expressed in sum-of-minterms form as given below.\[\begin{array}{l}f 1=\sum(0,2,3,5,7,8,11,13) \\f 2=\sum(1,3,5,7,11,...

Arjun

1.8k views

Arjun asked Feb 16

1 votes

3 answers

58

GATE CSE 2024 | Set 1 | Question: 54
Consider a digital logic circuit consisting of three $2$-to-$1$ multiplexers $\text{M1, M2}$, and $\text{M3}$ as shown below. $\mathrm{X} 1$ and $\mathrm{X} 2$ are inputs of $\mathrm{M} 1$. $\text{X3}$ and $\text{X4}$ are inputs ... the number of combinations of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ that give the output $\mathbf{Y}=\mathbf{1}$ is ____________.

Consider a digital logic circuit consisting of three $2$-to-$1$ multiplexers $\text{M1, M2}$, and $\text{M3}$ as shown below. $\mathrm{X} 1$ and $\mathrm{X} 2$ are inputs...

Arjun

2.1k views

Arjun asked Feb 16

65 votes

9 answers

59

GATE CSE 2017 Set 1 | Question: 7
The n-bit fixed-point representation of an unsigned real number $X$ uses $f$ bits for the fraction part. Let $i = n-f$. The range of decimal values for $X$ in this representation is $2^{-f}$ to $2^{i}$ $2^{-f}$ to $\left ( 2^{i} - 2^{-f} \right )$ 0 to $2^{i}$ 0 to $\left ( 2^{i} - 2^{-f} \right )$

The n-bit fixed-point representation of an unsigned real number $X$ uses $f$ bits for the fraction part. Let $i = n-f$. The range of decimal values for $X$ in this repres...

Arjun

16.6k views

Arjun asked Feb 14, 2017

27 votes

6 answers

60

GATE CSE 2002 | Question: 1.15
The $2's$ complement representation of the decimal value $-15$ is $1111$ $11111$ $111111$ $10001$

The $2's$ complement representation of the decimal value $-15$ is$1111$$11111$$111111$$10001$

Kathleen

10.0k views

Kathleen asked Sep 15, 2014

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