The information bit sequence {1 1 1 0 1 0 1 0 1} is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is $C(x) = x^4 + x + 1$. The encoded sequence of bits is ____.

Let $X(t) = A\cos(2\pi f_0 t+\theta)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of each other, and are uniformly distributed in the intervals $[-2,2]$ and $[0, 2\pi]$, respectively. $X(t)$ is fed to an 8-bit uniform mid-rise type quantizer.

Given that the autocorrelation of $X(t)$ is $R_X(\tau) = \frac{2}{3} \cos(2\pi f_0 \tau)$, the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is _________.

In the context of Bode magnitude plots, 40 dB/decade is the same as ______.

In the feedback control system shown in the figure below $G(s) = \dfrac{6}{s(s+1)(s+2)}$.

$R(s), Y(s),$ and $E(s)$ are the Laplace transforms of $r(t), y(t),$ and $e(t)$, respectively. If the input $r(t)$ is a unit step function, then __________