You are required to design and implement an arithmetic unit (AU) with the following ports: A and B are inputs, and are n-bit signed numbers represented in 2's complement F is 2-bit unsigned number for AU function selector R is the signed result represented in 2's complement. You will have to determine the minimum number of bits required for R such that an overflow never occurs. Below is a table that shows the arithmetic functions performed by the AU unit: Function Code AU Result F-00 F=01 F=10 F=11 R=A+B R=A-B R=2A-1 R = 4A (a) (2 points) Determine the size of R in bits such that overflow can never occur. (b) (8 points) Show the implementation of the AU using MSI components and the minimum number of additional gates. Hint: you will have to use some form of extension (zero- or sign-extension).