GATE EC 2014 Question Paper (16-Feb-2014) (Shift 2)

A 16-bit ripple carry adder is realized using 16 identical full adders (FA) as shown in the figure. The carry-propagation delay of each FA is 12 ns and the sum-propagation delay of each FA is 15 ns. The worst case delay (in ns) of this 16-bit adder will be __________.

An 8085 microprocessor executes “STA 1234H” with starting address location 1FFEH (STA copies the contents of the Accumulator to the 16-bit address location). While the instruction is fetched and executed, the sequence of values written at the address pins A₁₅ − A₈ is

A stable LTI system has a transfer function $H\left(s\right)=\frac{1}{s^2+s-6}$. To make this system causal and stable it needs to be cascaded with another LTI system having transfer function H₁(s). The correct choice for H1(s) is

A causal LTI system has zero initial conditions and impulse response ℎ(𝑡). Its input (𝑡) and output (𝑡) are related through the linear constant-coefficient differential equation

$\frac{d^{2}y\left(t\right)}{d{t}^2}+\alpha \frac{dy\left(t\right)}{dt}+{\alpha }^{2}y\left(t\right)=x\left(t\right)$.

Let another signal g(t) be defined as

$g\left(t\right)={\alpha }^2\underset{0}{\overset{t}{\int }}h\left(\tau \right)d\tau +\frac{dh\left(t\right)}{dt}+ah\left(t\right)$.

If G(s) is the Laplace transform of g(t), then the number of poles of G(s) is

The N-point DFT of a sequence x[n] ; 0 ≤ n ≤ N -1 is given by $\mathrm{X}\left[\mathrm{k}\right]=\frac{1}{\sqrt{\mathrm{N}}}\sum _{\mathrm{n}=0}^{\mathrm{N}-1}\mathrm{x}\left(\mathrm{n}\right){\mathrm{e}}^{\frac{-j2\pi \mathrm{nk}}{\mathrm{N}}};0\le \mathrm{k}\le \mathrm{N}-1$. Denote this relation as $\mathrm{X}\left[\mathrm{k}\right]=\mathrm{DFT}\left\{\mathrm{x}\left[\mathrm{n}\right]\right\}$. For N = 4 which one of the following sequences satisfies $\mathrm{DFT}\left(\mathrm{DFT}\left\{\mathrm{x}\left[\mathrm{n}\right]\right\}\right)=\mathrm{x}\left[\mathrm{n}\right]$