The block diagram of a linear time invariant system is given in Figure is (a) Write down the state variable equations for the system in matrix form assuming the state vector to be $${\left[ {{x_1}\left( t \right)\,\,{x_2}\left( t \right)} \right]^T}$$
(b) Find out the state transition matrix.
(c) Determine y(t), t ≥ 0, when the initial values of the state at time t = 0 are $${x_1}$$(0) = 1, and $${x_2}$$(0) = 1.

4-bit 2’s complement representation of a decimal number is 1000. The number is

If the input to the digital circuit (in the figure) consisting of a cascade of 20 XOR-gates is X then the output Y is equal to

The gates G₁ and G₂ in figure have propagation delays of 10nsec and 20nsec respectively. If the input V_i makes an abrupt change from logic 0 to 1 at time t = t₀, then the output waveform V₀ is