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 6= 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.

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.