Given the homogeneous state-space equation $$\mathop X\limits^ \bullet = \left[ {\matrix{ { - 3} & 1 \cr 0 & { - 2} \cr } } \right]x$$ the steady state value of $$\,\,{x_{ss}}\,\, = \mathop {Lim}\limits_{t \to \infty } x\left( t \right),$$ given the initial state value of $$x\left( 0 \right) = {\left[ {10 - 10} \right]^T},\,\,is$$

The output of a logic gate is $$''1''$$ when all its inputs are at logic $$''0''.$$ The gate is either

The output $$f$$ of the $$4$$- to- $$1$$ $$MUX$$ shown in fig. is

For the ring counter shown in Fig. find the steady state sequence if the initial state of the counters is $$1110\,\,(i.e.,\,\,{Q_3},{Q_2},{Q_1},{Q_0} = 1110).$$ Determine the MOD number of the counter.