Concurrent Error Detection in Multipliers by Using Reduced Wordlength Multiplication and Logarithms

Checking multiplication by using logarithms has already been proposed in literature but until now it has not been used widely in practice nor have different implementations been evaluated or compared. In this paper we will analyse the error detection capability of different implementations of logarithmic checking. Based on the results we propose a new way of checking multiplication. It uses normalised and word length reduced operands which are multiplied by a smaller multiplier in order to estimate the result of the multiplier to be checked. The estimated result is compared to the result of the multiplier by the difference of their base 2 logarithms. This approach enables the use of inaccurate approximations for the base 2 logarithm computation and improves error detection compared to standard logarithmic checking. The error detection capability can be adjusted to the application´s need for error detection by choosing the word length of the normalised operands. The error detection capability and the hardware overhead of this method are compared with the ones of known logarithmic checking methods.