A general proof for overlapped multiple-bit scanning multiplications

Because of recent advances in technology, multibit scanning implementations can be considered that exceed three-bit and four-bit groupings. The generalized proof for the multibit overlapped scanning multiplication is introduced, and the multiplication process is discussed. The proofs are intended to establish the correctness of the decode and the actions taken to produce the multiplication of any valid scheme proposed in the past, and to dictate the correct decode and actions taken for any overlapped s-bit scanning algorithm such that s is a natural number greater than or equal to two. The multiplication is considered to be between two fractional numbers, which are represented in two's-complement form.<>