Design a system that can invert one single bit in a $4-$bit input data, given its index. The index is a $2-$bit value that specifies which bit to invert in the $4-$bit input.

a$)(3$ pt$.)$ Draw a hierarchical design of the circuit using any kind of combinational logic blocks presented in class $($NOT$,$ BUF, AND, OR$,$ XOR, NAND, NOR, XNOR$).$ For each reused logic block, specify its exact name and size, and label its complete interface. Label the interface of the design circuit, too, matching the inputs and output. The output should be the modified $4-$bit value.