GATE EC 2014 Question Paper (16-Feb-2014) (Shift 1)

In the circuit shown, 𝑊 and 𝑌 are MSBs of the control inputs. The output 𝐹 is given by

If X and Y are inputs and the Difference (D = X – Y) and the Borrow (B) are the outputs, which one of the following diagrams implements a half-subtractor?

Let H₁(z) = (1 – pz⁻¹)⁻¹, H₂(z) = (1 – qz⁻¹)⁻¹, H(z) = H₁(z) + r H₂(z). The quantities p, q, r are real numbers. Consider $p=\frac{1}{2},q=-\frac{1}{4},\left|r\right|<1$. If the zero of H(z) lies on the unit circle, then r = ______

Let h(t) denote the impulse response of causal system with transfer function

$H\left(s\right)=\frac{1}{s+1}$

Consider the following three statements

S₁: The system is stable

S₂: $\frac{h\left(t+1\right)}{h\left(t\right)}$ is independent of time

S₃: A non – causal system with same transfer function is stable for the above system

The z-transform of the sequence x[n] is given by $X\left(z\right)=\frac{1}{{\left(1-2z^{-1}\right)}^2}$, with the region of convergence |z| > 2. Then x[2] is ______