Consider the equation $${\left( {123} \right)_5} = {\left( {x8} \right)_y}$$ with $$x$$ and $$y$$ as unknown. The number of possible solutions is _________.

The dual of a Boolean function $$F\left( {{x_1},{x_2},\,....,\,{x_n},\, + , \cdot ,'} \right),$$ written as $${F^D}$$, is the same expression as that of $$F$$ with $$+$$ and $$ \cdot $$ swapped. $$F$$ is said to be self-dual if $$F = {F^D} \cdot $$. The number of self-dual functions with $$n$$ Boolean variables is

Let $$k = {2^n}.$$ A circuit is built by giving the output of an ݊$$n$$-bit binary counter as input to an $$n$$-to-$${2^n}$$ bit decoder. This circuit is equivalent to a

The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functinal be denoted by p. Then 100p = __________________.