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1441
GATE ECE 2008 | Question: 20
Consider the amplitude modulated (AM) signal $A_{c} \cos \omega_{c} t+2 \cos \omega_{m} t \cos \omega_{c} t$. For demodulating the signal using envelope detector, the minimum value of $A_{c}$ should be $2$ $1$ $0.5$ $0$
Consider the amplitude modulated (AM) signal $A_{c} \cos \omega_{c} t+2 \cos \omega_{m} t \cos \omega_{c} t$. For demodulating the signal using envelope detector, the min...
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1442
GATE ECE 2008 | Question: 21
The Thevenin equivalent impedance $\text{Z}_{\text {th }}$ between the nodes $\text{P}$ and $\text{Q}$ in the following circuit is $1$ $1+s+\frac{1}{s}$ $2+s+\frac{1}{s}$ $\frac{s^{2}+s+1}{s^{2}+2 s+1}$
The Thevenin equivalent impedance $\text{Z}_{\text {th }}$ between the nodes $\text{P}$ and $\text{Q}$ in the following circuit is$1$$1+s+\frac{1}{s}$$2+s+\frac{1}{s}$$\f...
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1443
GATE ECE 2008 | Question: 22
The driving point impedance of the following network is given by $Z(s)=\frac{0.2 s}{s^{2}+0.1 s+2}$. The component values are $\begin{array}{lll} \mathrm{L}=5 \mathrm{~H}, & \mathrm{R}=0.5 \; \Omega, & \mathrm{C}=0.1 \mathrm{~F} \end{array}$ ...
The driving point impedance of the following networkis given by $Z(s)=\frac{0.2 s}{s^{2}+0.1 s+2}$. The component values are$\begin{array}{lll} \mathrm{L}=5 \mathrm{~H}, ...
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1444
GATE ECE 2008 | Question: 23
The circuit shown in the figure is used to charge the capacitor $\mathrm{C}$ alternately from two current sources as indicated. The switches $\text{S1}$ and $\text{S2}$ ... $\displaystyle{}\sum_{n=0}^{\infty}\left[0.5-e^{-(t-2 n T)}+0.5 e^{-(t-2 n T-T)}\right]$
The circuit shown in the figure is used to charge the capacitor $\mathrm{C}$ alternately from two current sources as indicated. The switches $\text{S1}$ and $\text{S2}$ a...
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1445
GATE ECE 2008 | Question: 24
The probability density function (PDF) of a random variable $\mathrm{X}$ is as shown below. The corresponding cumulative distribution function (CDF) has the form
The probability density function (PDF) of a random variable $\mathrm{X}$ is as shown below.The corresponding cumulative distribution function (CDF) has the form
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1446
GATE ECE 2008 | Question: 25
The recursion relation to solve $x=e^{-x}$ using Newton-Raphson method is $x_{n+1}=e^{-x_{n}}$ $x_{n+1}=x_{n}-e^{-x_{n}}$ $x_{n+1}=\left(1+x_{n}\right) \frac{e^{-x_{n}}}{1+e^{-x_{n}}}$ $x_{n+1}=\frac{x_{n}^{2}-e^{-x_{n}}\left(1+x_{n}\right)-1}{x_{n}-e^{-x_{n}}}$
The recursion relation to solve $x=e^{-x}$ using Newton-Raphson method is$x_{n+1}=e^{-x_{n}}$$x_{n+1}=x_{n}-e^{-x_{n}}$$x_{n+1}=\left(1+x_{n}\right) \frac{e^{-x_{n}}}{1+e...
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1447
GATE ECE 2008 | Question: 26
The residue of the function $f(z)=\dfrac{1}{(z+2)^{2}(z-2)^{2}}$ at $z=2$ is $-\;\frac{1}{32}$ $-\;\frac{1}{16}$ $\frac{1}{16}$ $\frac{1}{32}$
The residue of the function $f(z)=\dfrac{1}{(z+2)^{2}(z-2)^{2}}$ at $z=2$ is$-\;\frac{1}{32}$$-\;\frac{1}{16}$$\frac{1}{16}$$\frac{1}{32}$
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1448
GATE ECE 2008 | Question: 27
Consider the matrix $\mathbf{P}=\left[\begin{array}{cc}0 & 1 \\ -2 & -3\end{array}\right]$. The value of $\mathbf{e}^{\mathbf{P}}$ ...
Consider the matrix $\mathbf{P}=\left[\begin{array}{cc}0 & 1 \\ -2 & -3\end{array}\right]$. The value of $\mathbf{e}^{\mathbf{P}}$ is$\left[\begin{array}{cc}2 e^{-2}-3 e^...
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1449
GATE ECE 2008 | Question: 28
In the Taylor series expansion of $\exp (x)+\sin (x)$ about the point $x=\pi$, the coefficient of $(x-\pi)^{2}$ is $\exp (\pi)$ $0.5 \exp (\pi)$ $\exp (\pi)+1$ $\exp (\pi)-1$
In the Taylor series expansion of $\exp (x)+\sin (x)$ about the point $x=\pi$, the coefficient of $(x-\pi)^{2}$ is$\exp (\pi)$$0.5 \exp (\pi)$$\exp (\pi)+1$$\exp (\pi)-1$...
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1450
GATE ECE 2008 | Question: 29
$P_{X}(x)=M \exp (-2|x|)+N \exp (-3|x|)$ is the probability density function for the real random variable $X$, over the entire $x$ axis. $M$ and $N$ are both positive real numbers. The equation relating $M$ and $N$ is $M+\frac{2}{3} N=1$ $2 M+\frac{1}{3} N=1$ $M+N=1$ $M+N=3$
$P_{X}(x)=M \exp (-2|x|)+N \exp (-3|x|)$ is the probability density function for the real random variable $X$, over the entire $x$ axis. $M$ and $N$ are both positive rea...
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1451
GATE ECE 2008 | Question: 30
The value of the integral of the function $g(x, y)=4 x^{3}+10 y^{4}$ along the straight line segment from the point $(0,0)$ to the point $(1,2)$ in the $x\text{-}y$ plane is $33$ $35$ $40$ $56$
The value of the integral of the function $g(x, y)=4 x^{3}+10 y^{4}$ along the straight line segment from the point $(0,0)$ to the point $(1,2)$ in the $x\text{-}y$ plane...
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1452
GATE ECE 2008 | Question: 31
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at $s=-2$ and $s=-4$, and one simple zero at $s=-1$. A unit step $u(t)$ is applied at the input of the system. At steady state, the output has constant value of $1.$ The impulse response ... $[-0.5 \exp (-2 t)+1.5 \exp (-4 t)] u(t)$
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at $s=-2$ and $s=-4$, and one simple zero at $s=-1$. A unit ste...
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1453
GATE ECE 2008 | Question: 32
The signal $x(t)$ is described by $x(t)=\left\{\begin{array}{ll} 1 & \text { for }-1 \leq t \leq+1 \\ 0 & \text { otherwise } \end{array}\right.$ Two of the angular frequencies at which its Fourier transform becomes zero are $\pi, 2 \pi$ $0.5 \pi, 1.5 \pi$ $0, \pi$ $2 \pi, 2.5 \pi$
The signal $x(t)$ is described by$x(t)=\left\{\begin{array}{ll}1 & \text { for }-1 \leq t \leq+1 \\0 & \text { otherwise }\end{array}\right.$Two of the angular frequencie...
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1454
GATE ECE 2008 | Question: 33
A discrete time linear shift-invariant system has an impulse response $h[n]$ with $h[0]=1, h[1]=-1$, $h[2]=2$, and zero otherwise. The system is given an input sequence $x[n]$ with $x[0]=x[2]=1$, and zero otherwise. The number of nonzero samples in the output sequence $y[n]$, and the value of $y[2]$ are, respectively $5,2$ $6,2$ $6,1$ $5,3$
A discrete time linear shift-invariant system has an impulse response $h[n]$ with $h[0]=1, h =-1$, $h =2$, and zero otherwise. The system is given an input sequence $x[n]...
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1455
GATE ECE 2008 | Question: 34
Consider points $\mathrm{P}$ and $\mathrm{Q}$ in the $x\text{-}y$ plane, with $P=(1,0)$ and $Q=(0,1)$. The line integral $\displaystyle{}2 \int_{P}^{Q}(x d x+y d y)$ along the semicircle with the line segment $P Q$ as its diameter is $-1$ is $0$ is $1$ depends on the direction (clockwise or anti-clockwise) of the semicircle
Consider points $\mathrm{P}$ and $\mathrm{Q}$ in the $x\text{-}y$ plane, with $P=(1,0)$ and $Q=(0,1)$. The line integral $\displaystyle{}2 \int_{P}^{Q}(x d x+y d y)$ alon...
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1456
GATE ECE 2008 | Question: 35
Let $x(t)$ be the input and $y(t)$ be the output of a continuous time system. Match the system properties $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$ with system relations $\mathrm{R} 1, \mathrm{R} 2, \mathrm{R} 3, \mathrm{R} 4 .$ ... $\text{(P1, R3), (P2, R1), (P3, R2)}$ $\text{(P1, R1), (P2, R2), (P3, R3)}$
Let $x(t)$ be the input and $y(t)$ be the output of a continuous time system. Match the system properties $\mathrm{P} 1, \mathrm{P} 2$ and $\mathrm{P} 3$ with system rela...
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1457
GATE ECE 2008 | Question: 36
A memoryless source emits $n$ symbols each with a probability $p$. The entropy of the source as a function of $n$ increases as $\log n$ decreases as $\log (1 / n)$ increases as $n$ increases as $n \log n$
A memoryless source emits $n$ symbols each with a probability $p$. The entropy of the source as a function of $n$increases as $\log n$decreases as $\log (1 / n)$increases...
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1458
GATE ECE 2008 | Question: 37
$\{x(n)\}$ is a real-valued periodic sequence with a period N. $x(n)$ and $X(k)$ form $\mathrm{N}$-point Discrete Fourier Transform (DFT) pairs. The DFT $Y(k)$ of the sequence $\displaystyle{}y(n)=\frac{1}{N} \sum_{r=0}^{N-1} x(r) x(n+r)$ is $|X(k)|^{2}$ ... $\displaystyle{}\frac{1}{N} \sum_{r=0}^{N-1} X(r) X(k+r)$ $0$
$\{x(n)\}$ is a real-valued periodic sequence with a period N. $x(n)$ and $X(k)$ form $\mathrm{N}$-point Discrete Fourier Transform (DFT) pairs. The DFT $Y(k)$ of the seq...
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1459
GATE ECE 2008 | Question: 38
$\text{Group I}$ lists a set of four transfer functions. $\text{Group II}$ gives a list of possible step responses $y(t)$. Match the step responses with the corresponding transfer functions. $\textbf{Group I}$ \[ P=\frac{25}{s^{2}+25} \quad Q=\frac{36}{s^{2}+20 s+36} \quad R=\frac{36}{s^ ... $\text{P-2, Q-1, R-4, S-3}$ $\text{P-3, Q-4, R-1, S-2}$
$\text{Group I}$ lists a set of four transfer functions. $\text{Group II}$ gives a list of possible step responses $y(t)$. Match the step responses with the corresponding...
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1460
GATE ECE 2008 | Question: 39
A certain system has transfer function $G(s)=\dfrac{s+8}{s^{2}+\alpha s-4}$, where $\alpha$ is a parameter. Consider the standard negative unity feedback configuration as shown below. Which of the following statements is true? The closed loop ... , the closed loop system is stable. The closed loop system is stable for all values of $\alpha$, both positive and negative.
A certain system has transfer function $G(s)=\dfrac{s+8}{s^{2}+\alpha s-4}$, where $\alpha$ is a parameter. Consider the standard negative unity feedback configuration as...
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1461
GATE ECE 2008 | Question: 40
A signal flow graph of a system is given below. The set of equations that correspond to this signal flow graph is ...
A signal flow graph of a system is given below.The set of equations that correspond to this signal flow graph is$\dfrac{d}{d t}\left(\begin{array}{l}x_{1} \\ x_{2} \\ x_{...
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1462
GATE ECE 2008 | Question: 41
The number of open right half plane poles of $G(s)=\dfrac{10}{s^{5}+2 s^{4}+3 s^{3}+6 s^{2}+5 s+3}$ is $0$ $1$ $2$ $3$
The number of open right half plane poles of $G(s)=\dfrac{10}{s^{5}+2 s^{4}+3 s^{3}+6 s^{2}+5 s+3}$ is$0$$1$$2$$3$
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1463
GATE ECE 2008 | Question: 42
The magnitude of frequency response of an underdamped second order system is $5$ at $0 \; \mathrm{rad} / \mathrm{sec}$ and peaks to $\dfrac{10}{\sqrt{3}}$ at $5 \sqrt{2} \; \mathrm{rad} / \mathrm{sec}$. The transfer function of the system is $\frac{500}{s^{2}+10 s+100}$ $\frac{375}{s^{2}+5 s+75}$ $\frac{720}{s^{2}+12 s+144}$ $\frac{1125}{s^{2}+25 s+225}$
The magnitude of frequency response of an underdamped second order system is $5$ at $0 \; \mathrm{rad} / \mathrm{sec}$ and peaks to $\dfrac{10}{\sqrt{3}}$ at $5 \sqrt{2} ...
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1464
GATE ECE 2008 | Question: 43
$\text{Group I}$ gives two possible choices for the impedance $\mathrm{Z}$ in the diagram. The circuit elements in $\mathrm{Z}$ satisfy the condition $R_{2} C_{2}>R_{1} C_{1}$. The transfer function $\dfrac{V_{o}}{V_{i}}$ ... $\text{Q-1, R-2}$ $\text{Q-1, R-3}$ $\text{Q-2, R-3}$ $\text{Q-3, R-2}$
$\text{Group I}$ gives two possible choices for the impedance $\mathrm{Z}$ in the diagram. The circuit elements in $\mathrm{Z}$ satisfy the condition $R_{2} C_{2}>R_{1} C...
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1465
GATE ECE 2008 | Question: 44
For the circuit shown in the following figure, transistors $\text{M1}$ and $\text{M2}$ are identical $\text{NMOS}$ transistors. Assume that $\mathrm{M} 2$ is in saturation and the output is unloaded. The current $I_{X}$ is related to $I_{\text {bias }}$ ... $I_{X}=I_{\text {bias }}-\left(V_{D D}-\frac{V_{\text {out}}}{R_{E}}\right)$
For the circuit shown in the following figure, transistors $\text{M1}$ and $\text{M2}$ are identical $\text{NMOS}$ transistors. Assume that $\mathrm{M} 2$ is in saturatio...
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1466
GATE ECE 2008 | Question: 45
The measured transconductance $g_{m}$ of an $\text{NMOS}$ transistor operating in the linear region is plotted against the gate voltage $V_{G}$ at a constant drain voltage $V_{D}$. Which of the following figures represents the expected dependence of $g_{m}$ on $V_{G}?$
The measured transconductance $g_{m}$ of an $\text{NMOS}$ transistor operating in the linear region is plotted against the gate voltage $V_{G}$ at a constant drain voltag...
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1467
GATE ECE 2008 | Question: 46
Consider the following circuit using an ideal $\text{OPAMP}$. The $\text{I-V}$ characteristics of the diode is described by the relation $I=I_{0}\left(e^{\frac{V}{V_{T}}}-1\right)$ where $V_{T}=25 \; \mathrm{mV}, I_{0}=1 \; \mu \mathrm{A}$ and $\mathrm{V}$ is the ... $V_{o}$ is $0 \mathrm{~V}$ $0.1 \mathrm{~V}$ $0.7 \mathrm{~V}$ $1.1 \mathrm{~V}$
Consider the following circuit using an ideal $\text{OPAMP}$. The $\text{I-V}$ characteristics of the diode is described by the relation $I=I_{0}\left(e^{\frac{V}{V_{T}}}...
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1468
GATE ECE 2008 | Question: 47
The OPAMP circuit shown above represents a high pass filter low pass filter band pass filter band reject filter
The OPAMP circuit shown above represents ahigh pass filterlow pass filterband pass filterband reject filter
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1469
GATE ECE 2008 | Question: 48
Two identical $\text{NMOS}$ transistors $\text{M1}$ and $\text{M2}$ are connected as shown below. $\mathrm{V}_{\text {bias }}$ is chosen so that both transistors are in saturation. The equivalent $g_{m}$ ... transistors nearly equal to the $g_{m}$ of $\mathrm{Ml}$ nearly equal to $g_{m} / g_{o}$ of $\mathrm{M} 2$
Two identical $\text{NMOS}$ transistors $\text{M1}$ and $\text{M2}$ are connected as shown below. $\mathrm{V}_{\text {bias }}$ is chosen so that both transistors are in s...
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1470
GATE ECE 2008 | Question: 49
An $8085$ executes the following instructions $\begin{array}{lll} 2710 & \text { LXI} & \text{H,} & \text{30A0H } \\ 2713 & \text { DAD} & \text{H } \\ 2714 & \text { PCHL } \end{array}$ All addresses and constants are in Hex. ... $ \begin{array}{} \mathrm{PC}=6140 \mathrm{H} \\ \mathrm{HL}=2715 \mathrm{H} \end{array}$
An $8085$ executes the following instructions$\begin{array}{lll}2710 & \text { LXI} & \text{H,} & \text{30A0H } \\2713 & \text { DAD} & \text{H } \\2714 & \text { PCHL ...
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1471
GATE ECE 2008 | Question: 50
An astable multivibrator circuit using $\text{IC 555}$ timer is shown below. Assume that the circuit is oscillating steadily. The voltage $V_{C}$ across the capacitor varies between $3 \mathrm{V}$ to $5 \mathrm{V}$ $3 \mathrm{V}$ to $6 \mathrm{V}$ $3.6 \mathrm{V}$ to $6 \mathrm{V}$ $3.6 \mathrm{V}$ to $5 \mathrm{V}$
An astable multivibrator circuit using $\text{IC 555}$ timer is shown below. Assume that the circuit is oscillating steadily.The voltage $V_{C}$ across the capacitor vari...
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1472
GATE ECE 2008 | Question: 51
Silicon is doped with boron to a concentration of $4 \times 10^{17}$ atoms $/ \mathrm{cm}^{3}$. Assume the intrinsic carrier concentration of silicon to be $1.5 \times 10^{10} / \mathrm{cm}^{3}$ and the value of $\dfrac{k T}{q}$ to be $25 \; \mathrm{mV}$ ... $0.13 \; \mathrm{eV}$ goes down by $0.427 \; \mathrm{eV}$ goes up by $0.427 \; \mathrm{eV}$
Silicon is doped with boron to a concentration of $4 \times 10^{17}$ atoms $/ \mathrm{cm}^{3}$. Assume the intrinsic carrier concentration of silicon to be $1.5 \times 10...
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1473
GATE ECE 2008 | Question: 52
The cross section of a $\text{JFET}$ is shown in the following figure. Let $V_{G}$ be $-2 \mathrm{~V}$ and let $V_{P}$ be the initial pinch-off voltage. If the width $\mathrm{W}$ is doubled (with other geometrical parameters and doping levels remaining the same), then ... $\frac{1-\left(2 / \sqrt{V_{p}}\right)}{1-\left(1 /\left(2 \sqrt{V_{p}}\right)\right)}$
The cross section of a $\text{JFET}$ is shown in the following figure. Let $V_{G}$ be $-2 \mathrm{~V}$ and let $V_{P}$ be the initial pinch-off voltage. If the width $\ma...
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1474
GATE ECE 2008 | Question: 53
Consider the Schmidt trigger circuit shown below. A triangular wave which goes from $-12 \mathrm{~V}$ to $12 \mathrm{~V}$ is applied to the inverting input of the $\text{OPAMP}$. Assume that the output of the $\text{OPAMP}$ swings from $+15 \mathrm{~V}$ to $-15 \mathrm{~V}$. ... $+7.5 \mathrm{~V}$ $-5 \mathrm{~V}$ and $+5 \mathrm{~V}$ $0 \mathrm{~V}$ and $5 \mathrm{~V}$
Consider the Schmidt trigger circuit shown below.A triangular wave which goes from $-12 \mathrm{~V}$ to $12 \mathrm{~V}$ is applied to the inverting input of the $\text{O...
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1475
GATE ECE 2008 | Question: 54
The logic function implemented by the following circuit at the terminal $\text{OUT}$ is $\text{P NOR Q}$ $\text{P NAND Q}$ $\text{P OR Q}$ $\text{P AND Q}$
The logic function implemented by the following circuit at the terminal $\text{OUT}$ is$\text{P NOR Q}$$\text{P NAND Q}$$\text{P OR Q}$$\text{P AND Q}$
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1476
GATE ECE 2008 | Question: 55
Consider the following assertions. $\text{S1:}$ For Zener effect to occur, a very abrupt junction is required. $\text{S2:}$ For quantum tunneling to occur, a very narrow energy barrier is required. Which of the following is correct? Only $\text{S2}$ ... true and $\mathrm{S} 2$ is a reason for $\mathrm{S} 1$ Both $\text{S1}$ and $\text{S2}$ are false
Consider the following assertions.$\text{S1:}$ For Zener effect to occur, a very abrupt junction is required.$\text{S2:}$ For quantum tunneling to occur, a very narrow en...
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1477
GATE ECE 2008 | Question: 56
The two numbers represented in signed $2\text{'s}$ complement form are $\mathrm{P}=11101101$ and $\mathrm{Q}=11100110$. If $\mathrm{Q}$ is subtracted from $\mathrm{P}$, the value obtained in signed $2\text{'s}$ complement form is $100000111$ $00000111$ $11111001$ $111111001$
The two numbers represented in signed $2\text{'s}$ complement form are $\mathrm{P}=11101101$ and $\mathrm{Q}=11100110$. If $\mathrm{Q}$ is subtracted from $\mathrm{P}$, t...
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GATE ECE 2008 | Question: 57
Which of the following Boolean Expressions correctly represents the relation between $\text{P, Q, R}$ and $\mathrm{M}_{1}?$ $\text{M}_{1} = \text{(P OR Q) XOR R}$ $\text{M}_{1} = \text{(P AND Q) XOR R}$ $\text{M}_{1} = \text{(P NOR Q) XOR R}$ $\text{M}_{1} = \text{(P XOR Q) XOR R}$
Which of the following Boolean Expressions correctly represents the relation between $\text{P, Q, R}$ and $\mathrm{M}_{1}?$ $\text{M}_{1} = \text{(P OR Q) XOR R}$$\text{M...
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1479
GATE ECE 2008 | Question: 58
For the circuit shown in the following figure, $\mathrm{I}_{0}\text{-}\mathrm{I}_{3}$ are inputs to the $4: 1$ multiplexer. $\mathrm{R~(MSB)}$ and $\mathrm{S}$ are control bits. The output $\text{Z}$ ...
For the circuit shown in the following figure, $\mathrm{I}_{0}\text{-}\mathrm{I}_{3}$ are inputs to the $4: 1$ multiplexer. $\mathrm{R~(MSB)}$ and $\mathrm{S}$ are contro...
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GATE ECE 2008 | Question: 59
For each of the positive edge-triggered $\text{J-K}$ flip flop used in the following figure, the propagation delay is $\Delta T$. Which of the following waveforms correctly represents the output at $\mathrm{Q}_{1}?$
For each of the positive edge-triggered $\text{J-K}$ flip flop used in the following figure, the propagation delay is $\Delta T$.Which of the following waveforms correctl...
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Sep 17, 2022
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