$$P$$ is a $$16$$-bit signed integer. The $$2's$$ complement representtation of $$P$$ is $${\left( {F87B} \right)_{16}}$$ . The $$2's$$ complement representation of $$8{}^ * \,P$$ is

The minters expansion of $$f\left( {P,Q,R} \right) = PQ + Q\overline R + P\overline R $$ is

What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below?

The Boolean expression for the output $$f$$ of the multiplexer shown below is