When we were discussing floating point addition, we made the simplifying assumption that each of the functional units took the same amount of time. Suppose that fetch and store each take $2$ nanoseconds and the remaining operations each take $1$ nanosecond. a$.$ How long does a floating point addition take with these assumptions? b$.$ How long will an unpipelined addition of $1000$ pairs of floats take with these assumptions? c$.$ How long will a pipelined addition of $1000$ pairs of floats take with these assumptions? d$.$ The time required for fetch and store may vary considerably if the operands$/$results are stored in different levels of the memory hierarchy. Suppose that a fetch from a level $1$ cache takes $2$ nanoseconds, while a fetch from a level $2$ cache takes $5$ nanoseconds, and a fetch from main memory takes $50$ nanoseconds. What happens to the pipeline when there is a level $1$ miss and a level $2$ hit on a fetch of one of the operands? What happens when there is a level $1$ and a level $2$ miss?