Q$1]$ Design a combinational circuit that generates the $2\text{'}$s complement of a $3-$bit input binary number using:

a$)(40$ points$)$ Minimum number of basic logic gates $($NOT$,$ OR$,$ AND, XOR$).$

b$)(30$ points$)$ Using a decoder and any required logic gates.

c$)(30$ points$)$ Using only a decoder and an encoder.

Please sketch the design by hand