Consider the Boolean operator $$ \ne $$ with the following properties:
$$x \ne 0 = x,\,\,x \ne 1 = \overline x ,\,\,x \ne x = 0$$ and $$x \ne \overline x = 1.$$ Then $$x \ne y$$ is equivalent to

The $$16$$-bit $$2’s$$ complement representation of an integer is $$1111$$ $$1111$$ $$1111$$ $$0101;$$ its decimal representation is ____________.

Consider the recurrence relation $${a_1} = 8,\,{a_n} = 6{n^2} + 2n + {a_{n - 1}}.$$ Let $${a_{99}} = K \times {10^4}.$$ The value of $$K$$ is ____________.

The coefficient of $${x^{12}}$$ in $${\left( {{x^3} + {x^4} + {x^5} + {x^6} + ...} \right)^3}\,\,\,\,\,\,$$ is _____________.