Problem $1(15$ points$)$:

Suppose we have an ALU which always takes two inputs. Now we want to design a component based on the ALU. The component has four data inputs and one control source. The first data input, source$1,$ is used as one input of the ALU. The other input of the ALU is one of the other three data inputs of the component, source $2,$ source$3,$ and source $4$ based on the control source sel.

a$)$ Draw a black box for the ALU and add the required logic to implement the component. $(5$ points$)$

b$)$ Inside the ALU, we have an option to choose between Input$1$ and NOT$($Input$1)$ based on a control line c$1,$ and between Input$2$ and NOT$($Input$2)$ based on a control line c $2.$ Draw the required logic for the two selection operations in the ALU. $(5$ points$)$

c$)$ Finally, our ALU has three different instructions named $OR,$xOR, and AND and outputs one of the three results based on two selection lines named $op.$ Draw the required logic and combine it with what you get from b$)$ to show the logic inside the ALU. $(5$ points$)$