GATE EC 2014 Question Paper (15-Feb-2014) (Shift 2)

The output of the two flip-flops Q1, Q2 in the figure shown are initialized to 0, 0. The sequence generated at Q1 upon application of the clock signal is

For the 8085 microprocessor, the interfacing circuit to input 8-bit digital data (DI₀ – DI₇) from an external device is shown in the figure. The instruction for correct data transfer is

Consider a discrete-time signal

$x\left[n\right]=\{\begin{array}{c}nfor0\le n\le 10\\ 0otherwise\end{array}$

If y[n] is the convolution of x[n] with itself, the value of y[4] is ______

The input-output relationship of a causal stable LTI system is given as

y[n] = α y[n – 2] + β x[n]

If the impulse response h[n] of this system satisfies the condition $\sum _{n=0}^{\infty }h\left[n\right]=4,$ the relationship between α and β is

The value of the integral $\underset{-\infty }{\overset{\infty }{\int }}\sin c^2\left(5t\right)dt$ is ________