Logarithms reduce products to sums and powers to products; they play an important role in signal processing, communication and information theory. They are primarily

\r\nused for hardware calculations, handling multiplications, divisions,

\r\npowers, and roots effectively. There are three commonly

\r\nused bases for logarithms; the logarithm with base-10 is called

\r\nthe common logarithm, the natural logarithm with base-e and

\r\nthe binary logarithm with base-2. This paper demonstrates different

\r\nmethods of calculation for log2 showing the complexity

\r\nof each and finds out the most accurate and efficient besides

\r\ngiving insights to their hardware design. We present a new

\r\nmethod called Floor Shift for fast calculation of log2, and

\r\nthen we combine this algorithm with Taylor series to improve

\r\nthe accuracy of the output, we illustrate that by using two

\r\nexamples. We finally compare the algorithms and conclude

\r\nwith our remarks.<\/p>\r\n","references":"[1] H. Hassler and N. Takagi, Function evaluation by table look-up and\r\naddition, in Proc.12th Symp.on Computer Arithmetic, pp. 10-16, Jul.1995.\r\n[2] D. DasSarma, D.W. Matula, Measuring the Accumcy of ROM Reciprocal\r\nTables, IEEE 11th Symp.on Computer Arithmetic, pp.932-940, Aug.1994.\r\n[3] Pramod K. Meher, Javier Valls, Tso-Bing Juang, K. Sridharan and\r\nKoushik Maharatna, 50 Years of CORDIC: Algorithms, Architectures and\r\nApplications, Circuits and Systems I: Regular Papers, IEEE Transactions\r\non (Volume:56, Issue: 9).\r\n[4] Liu Bangqiang, He Ling, Yan Xiao, Base-N Logarithm Implementation\r\non FPGA for the Data with Random Decimal Point Positions, (2013 IEEE\r\n9th International Colloquium on Signal Processing and its Applications,\r\n8-10 Mac. 2013, Kuala Lumpur, Malaysia)\r\n[5] Kostopoulos, D.K, An algorithm for the computation of binary logarithms,\r\nComputers, IEEE Transactions on (Volume:40 , Issue: 11).\r\n[6] Tropea, S.E, FPGA Implementation of Base-N Logarithm, Programmable\r\nLogic, 2007. SPL07. 2007 3rd Southern Conference.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 94, 2014"}