Mathematically design an algorithm which, given two binary numerals 1 . . . 10 and1 . . . 10, computes the binary numeral1 . . . 10 representing their product. Note that we have not specified the maximum size of these numerals. Your algorithm must follow the same digit-by-digit approach as long multiplication. You should express the algorithm in terms of basic operations that are possible on sequences of bits, such as single-bit operations, and rearranging,

removing, or adding bits. You can also assume that an addition operation is available, so you can take two binary numerals of arbitrary size and get their sum as a binary numeral 1 . . . 10 = 1 . . . 10 + 1 . . . 10. To develop this algorithm, you may need to introduce multiple helper functions to do simpler tasks; that is part of your job in this question. For each such helper functions you define, you must also provide a mathematically precise specification