The ideas behind the Karatsuba algorithm can be applied to multiply things other than decimal integers. Provide an algorithm to compute the product of two n-bit binary numbers which works in O(n^log2 3) time. Prove that the algorithm returns the product of its inputs and that the algorithm runs in O(n^log2 3) time. Assume that any arithmetic operations (e.g., addition, multiplication) between two bits can be done in constant time and that n is a power of 2.