Low Cost Serial Multipliers for High-Speed Specialised Processors

This paper presents four new arrays for signed number multiplication and multiplication/ addition. In these structures, it is assumed that the factors are expressed in 2's complement while the addend and the result are expressed in redundant notation. Two arrays operate in a serial-parallel way, since one of the factors 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. The other two arrays are fully serial because all the input numbers are processed digit by digit, starting with the most signifcant one. In all the arrays presented the results are produced in a serial manner from left to right. The arithmetic units introduced in this paper can be used as basic blocks of special purpose processors performing functions such as non-recursive digital filtering, signal correlation and matrix multiplication. It is shown that our units achieve the same speed advantages as other similar units which use redundant representations for the results, with a cost equivalent to their counterparts based on full 2's complement representation.