
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
D.K. Kostopoulos, "An Algorithm for the Computation of Binary Logarithms," IEEE Transactions on Computers, vol. 40, no. 11, pp. 12671270, November, 1991.  
BibTex  x  
@article{ 10.1109/12.102831, author = {D.K. Kostopoulos}, title = {An Algorithm for the Computation of Binary Logarithms}, journal ={IEEE Transactions on Computers}, volume = {40}, number = {11}, issn = {00189340}, year = {1991}, pages = {12671270}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.102831}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  An Algorithm for the Computation of Binary Logarithms IS  11 SN  00189340 SP1267 EP1270 EPD  12671270 A1  D.K. Kostopoulos, PY  1991 KW  binary logarithms computation; algorithm; base2 logarithm; binary number; baseN; microcode; iterations; algorithm theory; digital arithmetic. VL  40 JA  IEEE Transactions on Computers ER   
The author presents a simple algorithm for the computation of the base2 logarithm of a given binary number. The concept can be easily extended to baseN. Unlike other methods, this is not a curve fitting of the base2 logarithm of a given binary number. The algorithm constitutes a simple stepbystep, bitbybit, computation of the logarithm of binary numbers. It can be easily implemented in simple microcode, and offers precision that is proportional to the number of performed iterations. Thus, it asymptotically converges to the true logarithm of the given number.
[1] E. L. Hall, D. D. Lynch, and S. J. Dwyer III, "Generation of products and quotients using approximate binary logarithms for digital filtering applications,"IEEE Trans. Comput., vol. C19, pp. 97105, Feb. 1970.
[2] T. Kurokawa, J. A. Payne, and S. C. Lee, "Error analysis of recursive digital filters implemented with logarithmic number systems,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP28, pp. 706715, Dec. 1980.
[3] N. G. Kingsbury and P. J. W. Rayner, "Digital filtering using logarithmic arithmetic"Electron. Lett., vol. 7, no. 2, pp. 5658, Jan. 1971.
[4] M. H. Etzel, Bell Laboratories, "Logarthimics addition for digital signal processing applications,"IEEE Trans. Circuits Syst., vol. CAS32, pp. 694697.
[5] H.Y. Lo "Binary logarithms for computing integral and nonintegral roots and powers,"Int. J. Electron., vol. 40, no. 4, pp. 357364, 1976.
[6] J. N. Mitchell, Jr., "Computer multiplication and division using binary logarithms,"IRE Trans. Electron. Comput., pp. 512517, Aug. 1962.
[7] G. W. Gerrity, "Computer representation of real numbers,"IEEE Trans. Comput., vol. C31, no. 8, pp. 709714, Aug. 1982.
[8] J. H. Lang, C. A. Zukowski, R. O. LaMaire, and C. H. An, "Integratedcircuit logarithmic arithmetic units,"IEEE Trans. Comput., vol. C34, pp. 475483, May 1985.
[9] T. A. Brubaker and J. C. Becker, "Multiplication using logarithms implemented with readonly memory,"IEEE Trans. Comput., vol. C24, pp. 761765, Aug. 1975.
[10] F. J. Taylor, "An extended precision logarithmic number system,"IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP31, pp. 231233, Feb. 1983.
[11] S. C. Lee and A. D. Edgar, "The focus number system,"IEEE Trans. Comput., vol. C26, pp. 11671170, Nov. 1977.
[12] F. J. Taylor, "A hybrid floatingpoint logarithmic number system processor,"IEEE Trans. Circuits Syst., vol. CAS32, pp. 9295, Jan. 1985.
[13] M. Combet, H. Van Zonneveld, and L. Verbeek, "Computation of the base two logarithm of binary numbers,"IEEE Trans. Electron. Comput., vol. EC14, pp. 863867, Dec. 1965.
[14] D. Marino, "New algorithms for the approximate evaluation in hardware of binary logarithms and elementary functions,"IEEE Trans. Comput., vol. C21, pp. 14161421, Dec. 1972.
[15] T. C. Chen, "Automatic computation of exponential, logarithms, rations and square roots,"IBM J. Res. Develop., pp. 380388, July 1972.
[16] E. E. Swartzlander, Jr., and A. G. Alexopoulos, "The sign logarithm number system,"IEEE Trans. Comput., vol. C24, pp. 12381242, Dec. 1975.
[17] H.Y. Lo and Y. Aoki, "Generation of a precise binary logarithm with difference grouping programmable logic array,"IEEE Trans. Comput., vol. C34, pp. 681691, Aug. 1985.
[18] S.Y. Shi, "Shortcut to logarithms combines table lookup and computation,"Comput. Design, pp. 186189, May 1976.
[19] J. C. Majithia and D. Levan, "A note on base2 logarithm computations,"Proc. IEEE, pp. 15191520, 1973.
[20] Lo and Chen, "A hardwired generalized algorithm for generating the logarithm basekby iteration,"IEEE Trans. Comput., vol. C36, pp. 13631367, Nov. 1987.