The state variable representation of a system is given as $$$\eqalign{ & \mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 \cr 0 & { - 1} \cr } } \right]x;x\left( 0 \right) = \left[ {\matrix{ 1 \cr 0 \cr } } \right] \cr & y = \left[ {\matrix{ 0 & 1 \cr } } \right]x \cr} $$$

The response y(t) is

A function of Boolean variables X,Y and Z is expressed in terms of the min-terms as F(X, Y, Z)=$$\sum\limits_{}^{} {} $$m(1,2,5,6,7) Which one of the product of sums given below is equal to the funtion F(X, Y, Z)?

In the figure shown, the output ܻ is required to be ܻ Y=AB+ $$\overline C $$$$\overline D $$. The gates G1 and G2 must be, respectively,

A 1-to-8 demultiplexer with data input D$$_{in}$$ , address inputs S$$_{0}$$, S$$_{1}$$, S$$_{2}$$ (with S$$_{0}$$ as the LSB) and $${\overline Y _0}$$ to $${\overline Y _7}$$ as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with enable input $$\overline E $$ and address inputs A$$_{0}$$ and A$$_{1}$$) as shown in the figure. $${D_{in}}$$, S$$_{0}$$, S$$_{1}$$and S$$_{2}$$ are to be connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P, Q, R, and S terminals should be