A Novel Decimal Logarithmic Converter Based on First-Order Polynomial Approximation

• Published in: Circuits, systems, and signal processing Vol. 31; no. 3; pp. 1179 - 1190
• Main Authors: Chen, Dongdong, Ko, Seok-Bum
• Format: Journal Article
• Language: English
• Published: Boston SP Birkhäuser Verlag Boston 01.06.2012; Springer Nature B.V
• Subjects: Algorithms; Approximation; Circuits and Systems; Conversion; Converters; Decimals; Electrical Engineering; Electronics and Microelectronics; Engineering; Hardware; Instrumentation; Integrated circuits; Mathematical analysis; Polynomials; Short Paper; Signal,Image and Speech Processing; Tables (data); First-order polynomial approximation; Decimal computer arithmetic; Decimal logarithmic converter; FPGA
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-011-9365-y

This paper presents a decimal logarithmic converter based on the decimal first-order polynomial (linear) approximation algorithm. The proposed approach is mainly based on a look-up table, followed a decimal linear approximation step. Compared with a binary-based decimal linear approximation algorithm (Algorithm 1), the proposed algorithm (Algorithm 2) is error-free in the conversion between the decimal and the binary formats. The proposed architecture is implemented by the combinational logic in the binary coded decimal (BCD) encoding on Virtex5 XC5VLX110T FPGA. The results of the comparison show that the hardware performance of Algorithm 2 can run 2.15 times faster than Algorithm 1, with the expense of 1.14 times more area.