The transfer function Y(s)/U(s) of a system described by the state equations
$$\mathop x\limits^ \bullet $$(t) = -2x(t)+2u(t)
y(t) = 0.5x(t) is

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.

The number of comparators required in a 3-bit comparator type ADC is

It is required to design a binary mod-5 synchronus counter using AB flip-flops such that the output Q₂Q₁Q₀ changes as $$000 \to 001 \to 010$$ ........and so on. The excitation table for the AB flip-flops is given in the table

(a) Write down the state table for the mod-5 counter.
(b)Obtain simplified SOP expressions for the inputs A₂, B₂, A₁, B₁, A₀ and B₀ in terms of Q₂, Q₁, Q and their complements.
(c) Hence, complete the circuit diagram for the mod-5 counter given in the figure using minimum number of 2-input NAND-gate only.