In one step of base-10 scientific notation to base-2 scientific notation, we need to make numbers (in base-2) as large as possible before division by 10. This is to minimize the error due to integer division.

We can use 64-bit unsigned integers in most of the calculations. As such, it is important to find the largest multiplier to a known value so that the product the multiplier (a power of 2) and the known value is as large as possible but not to exceed the largest value that can be represented by a 64-bit unsigned integer.

This issue is further complicated by the fact that we need to add 5 before division by 10. This means we are looking for the largest natural number p such that ( x 2 p + 5 ) ( 2 64 1 ) where x is the value given.

What is the value of this p when x =1,149,376?

After thought: when you do this by hand, you can use a calculator and use the log functions. However, to do this quickly in a program, it is best to avoid any use of log functions. Think about how you can do this with only integer operations.