Improved fixed-width multiplier

Niniejszy artykuł prezentuje nową metodę kompensacji błędu odcięcia dla mnożenia o stałej szerokości bitowej czyli takiej, dla której szerokość bitowa argumentów wejściowych jest taka sama jak wyjścia. Niektóre poprzednie publikacje były oparte na błędnych założeniach, dlatego zadaniem tej publikacji jest wykazanie wspomnianych błędów oraz zaprezentowanie nowej architektury, dla której błąd średni dąży do zera.Multiplication is usually implemented in hardware as a full bit-width parallel multiplier, i.e., input bit-widths add up to make up the output bit-width. Nevertheless, in most real-world cases, the input bit-width n is the same as the output bit-width. Therefore, in order to reduce a multiplier area, the n LSBs columns of the multiplier are truncated during the multiplication process (see Fig. 1). This introduces a truncation error which can be reduced by an error compensation circuit. The truncation errors presented in the previous papers, e.g. [3, 6, 7], are based on the false assumption; during truncation error calculation it is sufficient to consider only the combination of each partial input bit products aibj. instead of ever input bits ai and bj (see Fig. 2 and Tab. 1). Therefore a proper fixed-width multiplier structure should be introduced (the old one should be redesigned). This paper focuses on optimizing the mean error (ME) of the truncated multiplier. As a result, a novel Improved Variable error Compensation Truncated Multiplier (IVCTM) is proposed which in comparison to [2], reduces the number of AND gates by 1 in the error compensation circuit (see Fig. 3). For the IVCTM, a mean error is significantly lower than for previously published counterparts. The structure of the IVCTM is simplified in comparison to the previously published truncated multiplier [2], therefore it occupies less silicon area