Design an algorithm that will use simple arithmetic operations to estimate the base-2 logarithm of a given positive number. The algorithm should report the exact answer if it is an integer and otherwise state upper and lower bounds for it. For example, given the input 256 your algorithm should report 8, and given the input 81 your algorithm should report the logarithm lies between 6 and 7. Note that numbers less than 1 but greater than zero are positive. (Your solution may not invoke a log function/operator.)