GATTACA, year $2060$: Biomedical sciences are in their very best moment; the online DNA

analysis has replaced ID$,$ driver license and VISA cards. Recently some researchers have

discovered the "intelligence gene" and now it's known that the gene corresponds to the

sequence GGTC$.$ Your company has decided to design a hardware module able to detect this

gene in a quick way, in order to include it in the DNA readers used to identify citizens.

Each DNA sequence's base $(=$ each letter$)$ is encoded with $2$ bits according to the following

table:

A: Adenina, G: Guanina, C: Cytozyna, T: Tymina

The module that we want to design has $2$ inputs $x1,x0$ and one output out. A logical $1$ should

be generated any time the sub$-$sequence GGTC is detected, as the following image shows.

Design this module.