The state transition matrix for the system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 1 \cr 1 \cr } } \right]u$$ is

The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{ { - 1} & 1 \cr 0 & { - 3} \cr } } \right]\,\,Q = \left[ {\matrix{ 0 \cr 1 \cr } } \right]$$
$$R = \left[ {\matrix{ 0 & 1 \cr } } \right]$$ The system has the following controllability and observability properties:

The $$SOP$$ (sum of products) from of a Boolean function is $$\sum \left( {0,1,3,7,11} \right),$$ where inputs are $$A,B,C,D$$ ($$A$$ is $$MSB$$, and $$D$$ is $$LSB$$). The equivalent minimized expression of the function is

A $$JK$$ flip flop can be implemented by $$T$$ flip flops. Identify the correct implementation.