Base-N logarithm implementation on FPGA for the data with random decimal point positions

Logarithmic transformation is an important part of many digital signals processing system, especially in the fields of instruments design. This paper gives details on a simple way based on CORDIC algorithm and the idea of data initialization to implement logarithmic transformation. Given the number of bits for input data, we can get the corresponding base-N logarithmic results after we specify their decimal point positions at will. The logarithmic converter introduced by this paper is able to support the logarithmic transformation of data with the number of bits up to 48.