Question $1$: a$)$ Design a combinational circuit that takes two three$-$bit binary numbers A and B$,$ processes them, and generates the output functions X and Y if: X$=1$ if binary number A is the $2\text{'}$s complement of binary number B$.$Y$=1$ if the binary number B is a multiple of three. For this you are asked:Build the truth table.

Represent the functions X$,$ Y according to the POS and SOP scheme.

Simplify the output variables using the Theorems of Boolean Algebra. Simplify using Karnaugh Maps. Implement using digital gates.

b$)$ using figure $2$ implement the truth table of problem $1$:only with NAND gates. Only with NOR gates.