2. (12 marks] A friend proposes the following scheme for representing rational numbers numbers that can be represented as a/b, where a and b are both integers and b + 0) using 16 bits. The leftmost 9 bits will be the signed binary integer a; the rightmost 7 bits will be the unsigned binary integer b. a. [2 marks] What is the largest value representable using this scheme? b. [2 marks What is the smallest positive (non-zero) value representable using this scheme? c. [2 marks What's the smallest (i.e., most negative) value representable using this scheme? d. [2 marks] Give a pair of distinct bit patterns that both represent the same non-zero value under this scheme. e. [2 marks Give an unusable bit pattern under this scheme (a pattern that does not represent a rational number). f. [2 marks] Propose a change to the scheme that keeps it simple but increases the number of distinct values representable