I don't think anyone has mentioned that the multiplier you are using in your machine is almost certainly using an expanded digit set, multiplying by the digits {-2, -1, 0, 1, 2} rather than {0,1,2,3} in bit pairwise fashion. Pairwise multiplication reduces the number of partial products, and eliminating the x3 multiplication makes it easy to compute the partial products. Conversion of radix 4 {0, 1, 2, 3} to radix 4 {-2, -1, 0, 1, 2} can be done with no carries, and is desirable from a hardware standpoint. These are called Booth multipliers. The inverse process can and often is used to derive an expanded digit version of a quotient.