Efficient serial-parallel arrays for multiplication and addition

Three new arrays for unsigned and signed multiplication, and for multiplication/addition are presented. It is assumed that the factors are axpressed in 2's complement, while the addend (in the latter array only) and the result are expressed in a redundant notation. The arrays operate in serial-parallel way, since one factor is input in parallel, while the second factor and the addend (in the case of multiplication/addition) are entered digit by digit starting from the most significant one; the result is also produced serially with the most significant digit first. Hence, the arithmetic unit presented is suitable to be used as basic block of special purpose processors performing functions such as non-recursive digital filtering, signal correlation and matrix multiplication. Indeed, they have the same speed improvements as other similar units using redundant representations for the result, with a cost equivalent to their counterparts based on full 2's complement representation.