A linear time-invariant system is described by the state variable model $$$\left[ {\matrix{ {{{\mathop x\limits^ \bullet }_1}} \cr {{{\mathop x\limits^ \bullet }_2}} \cr } } \right] = \left[ {\matrix{ { - 1} & 0 \cr 0 & { - 2} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] + \left[ {\matrix{ 0 \cr 1 \cr } } \right]u.$$$ $$$Y = \left[ {\matrix{ 1 & 2 \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$$

The logic realized by the circuit shown in figure is

A combinational circuit has three inputs A, B and C and an output F. F is true only for the following input combinations?

A is false and B is true
A is false and C is true
A, B and C are all false
A, B and C are all true.

(a)Write the truth table for F. use the convention, true = 1 and false = 0.
(b)Write the simplified expression for F as a Sum of Products.
(c) Write the simplified expression for F as a product of Sums.
(d) Draw a logic circuit implementation of F using the minimum number of 2 input NAND gates only.

The initial contents of the 4-bit serial-in-parallel-out, right-shift, Shift Register shown in figure is 0110. After three clock pulses are applied, the contents of the Shift Register will be