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Taxonomy of Decimal Multiplier Research

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Algorithms and Applications

Abstract

Decimal arithmetic hardware research accelerated in the last decade with introduction of decimal floating point formats in “IEEE 754-2008” standards. During the revision phase (IEEE 754R), 2000–2008, global research on decimal arithmetic witnessed state-of-the-art decimal hardware proposals as well as software routines for decimal computations on general-purpose microprocessors. Multiplication forms a fundamental arithmetic operation and an integral part of arithmetic hardware units. This paper provides taxonomy of the major contributions in decimal multiplier research.

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References

  1. Schmid, H.: Decimal Computation. Wiley (1974)

    Google Scholar 

  2. Richards, R.: Arithmetic Operations in Digital Computers. D. Van Nostrand Company, Inc. (1955)

    Google Scholar 

  3. Vazquez, A., Antelo, E., Montuschi, P.: Improved design of high-performance parallel decimal multipliers. IEEE Trans. Comput. 59(5), 679–693 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Erle, M., Hickmann, B., Schulte, M.: Decimal floating-point multiplication. IEEE Trans. Comput. 58(7), 902–916 (2009)

    Google Scholar 

  5. Cornea, M., Anderson, C., Harrison, J., Tang, P., Schneider, E., Tsen, C.: A software implementation of the IEEE 754R decimal floating-point arithmetic using the binary encoding format. In: 18th IEEE Symposium on Computer Arithmetic, 2007. ARITH ‘07, Montepellier, pp. 29–37 (2007)

    Google Scholar 

  6. Cornea, M.: Intel® Decimal Floating-Point Math Library. Intel® Corporation (2011)

    Google Scholar 

  7. JAVA, Sun Microsystems: Class BigDecimal Documentation. JAVA (1996)

    Google Scholar 

  8. Cowlishaw, M.: The decNumber C Library, Version 3.68., IBM (January 2010)

    Google Scholar 

  9. Simington, R.: The intel 8087 numerics processor extension. BYTE Mag. 8(4), 154 (1983)

    Google Scholar 

  10. Cowlishaw, M.: Decimal floating-point: algorism for computers. In: Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH’03), pp. 104–111 (2003)

    Google Scholar 

  11. Erle, M., Schulte, M., Linebarger, J.: Potential speedup using decimal floating-point hardware. In: Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002, Pacific Grove, CA, USA, vol. 2, pp. 1073–1077, Nov 2002

    Google Scholar 

  12. Webb, C.: IBM z10: the next-generation mainframe microprocessor. IEEE Micro 28(2), 19–29 (2008)

    Google Scholar 

  13. Raafat, R., Abdel-Majeed, A., Samy, R., ElDeeb, T., Farouk, Y., Elkhouly, M., Fahmy, H.: A decimal fully parallel and pipelined floating point multiplier. In: 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, pp. 1800–1804 (2008)

    Google Scholar 

  14. Fahmy, H., ElDeeb, T., Hassan, M.: Decimal floating point for future processors. In: International Conference on Microelectronics (ICM), Cairo, pp. 443–446 (2010)

    Google Scholar 

  15. Cowlishaw, M.: Densely packed decimal encoding. Comput. Digit. Techn. 149(3), 102–104 (2002)

    Article  Google Scholar 

  16. IEEE Computer Society: IEEE Standards for Floating-Point Arithmetic 754-2008, IEEE. Aug 2008

    Google Scholar 

  17. Quach, N., Takagi, N., Flynn, M.: Systematic IEEE rounding method for high-speed floating-point multipliers. IEEE Trans. Very Larg. Scale Integr. VLSI Syst. 12(5), 511–521 (2004)

    Article  Google Scholar 

  18. Even, G., Seidel, P.: A comparison of three rounding algorithms for IEEE floating-point multiplication. IEEE Trans. Comput. 49(7), 638–650 (2000)

    Article  Google Scholar 

  19. Wang, L.-K., Schulte, M.: Decimal floating-point adder and multifunction unit with injection-based rounding. In: 18th IEEE Symposium on Computer Arithmetic, 2007. ARITH ‘07, Montepellier, pp. 56–68 (2007)

    Google Scholar 

  20. Wang, L.-K., Schulte, M., Thompson, J., Jairam, N.: Hardware designs for decimal floating-point addition and related operations. IEEE Trans. Comput. 58(3), 322–335 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Tsen, C., Gonzalez-Navarro, S., Schulte, M., Hickmann, B., Compton, K.: A combined decimal and binary floating-point multiplier. In: 2009 20th IEEE International Conference on Application-specific Systems, Architectures and Processors, Boston, MA, pp. 8–15 (2009)

    Google Scholar 

  22. Tsen, C., Schulte, M., Gonzalez-Navarro, S.: Hardware design of a binary integer decimal-based IEEE P754 rounding unit. In: IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP) 2007, Montreal, Que, pp. 115–121 (2007)

    Google Scholar 

  23. Camina, S.: A comparison of taxonomy generation techniques using Bibliometric. EECS Thesis, Massachusetts Institute of technology (2010)

    Google Scholar 

  24. Guardia, C.: Implementation of a fully pipelined BCD multiplier in FPGA. In: VIII Southern Conference on Programmable Logic (SPL), 2012, Bento Goncalves, pp. 1–6 (2012)

    Google Scholar 

  25. Carlough, S., Schwarz, E.: Decimal Multiplication using Digit Recoding. US, Patent US 7136893 B2, US. 14 Nov 2006

    Google Scholar 

  26. Baesler, M., Teufel, T.: FPGA implementation of a decimal floating-point accurate scalar product unit with a parallel fixed-point multiplier. In: International Conference on Reconfigurable Computing and FPGAs 2009, Quintana Roo, pp. 6–11 (2009)

    Google Scholar 

  27. Erle, M., Schulte, M.: Decimal multiplication via carry-save addition. In: Proceedings IEEE International Conference on Application-Specific Systems, Architectures, and Processors, pp. 348–358 (2003)

    Google Scholar 

  28. Croy, J.: Improved arrangement of a decimal multiplier. IRE Trans. Electron. Comput. EC-9(2), 263 (1960)

    Google Scholar 

  29. Han, L., Ko, S.-B.: High-speed parallel decimal multiplication with redundant internal encodings. IEEE Trans. Comput. 62(5), 956–968 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  30. Castellanos, I., Stine, J.: Decimal partial product generation architectures. In: 51st Midwest Symposium on Circuits and Systems 2008, Knoxville, TN, pp. 962–965 (2008)

    Google Scholar 

  31. Bozdas, K., Alkar, A.: Analysis on the column sum boundaries of decimal array multipliers. In: IEEE 55th International Midwest Symposium on Circuits and Systems (MWSCAS) 2012, Boise, ID, pp. 318–321 (2012)

    Google Scholar 

  32. Erle, M., Schulte, M., Hickmann, B.: Decimal floating-point multiplication via carry-save addition. In: 18th IEEE Symposium on Computer Arithmetic, 2007. ARITH ‘07, Montepellier, pp. 46–55. June 2007

    Google Scholar 

  33. Dadda, L., Nannarelli, A.: A variant of a Radix-10 combinational multiplier. In: IEEE International Symposium on Circuits and Systems (ISCAS 2008), pp. 3370–3373 (2008)

    Google Scholar 

  34. Hickman, B., Krioukov, A., Schulte, M., Erle, M.: A parallel IEEE P754 decimal floating-point multiplier. In: 25th International Conference on Computer Design, 2007. ICCD 2007. Lake Tahoe, CA, pp. 296–303 (2007)

    Google Scholar 

  35. Gorgin, S., Jaberipur, G.: Sign-magnitude encoding for efficient VLSI realization of decimal multiplication. IEEE Trans. Very Larg. Scale Integr. (VLSI) Syst. (99), 1–13 (2016)

    Google Scholar 

  36. Erle, M., Hickmann, B.: Combined binary/decimal fixed-point multiplier and method. US, Patent US8577952 B2, US. 5 Nov 2013

    Google Scholar 

  37. Dadda, L., Pisoni, M., Santambrogio, M.: A parallel-serial decimal multiplier architecture. In: IEEE 15th International Conference on Computational Science and Engineering (CSE), 2012, Nicosia, pp. 310–317 (2012)

    Google Scholar 

  38. Hickmann, B., Schulte, M., Erle, M.: Improved combined binary/decimal fixed-point multipliers. In: IEEE International Conference on Computer Design, 2008. ICCD 2008. Lake Tahoe, CA, pp. 87–94 (2008)

    Google Scholar 

  39. Gorgin, S., Jaberipur, G.: Fully redundant decimal arithmetic. In: 2009 19th IEEE International Symposium on Computer Arithmetic, pp. 145–152 (2009)

    Google Scholar 

  40. Jaberipur, G., Kaivani, A.: Binary-coded decimal digit multipliers. IET Comput. Digit. Tech. 1(4), 377–381 (2007)

    Article  Google Scholar 

  41. Jaberipur, G., Kaivani, A.: Improving the speed of parallel decimal multiplication. IEEE Trans. Comput. 58(11), 1539–1552 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  42. James, R., Jacob, K., Sasi, S.: High performance, low latency double digit decimal multiplier on ASIC and FPGA. In: World Congress on Nature and Biologically Inspired Computing, 2009. NaBIC 2009, Coimbatore, pp. 1445–1450 (2009)

    Google Scholar 

  43. James, R., Shahana, T., Jacob, K., Sasi, S.: Decimal multiplication using compact BCD multiplier. In: Electronic Design, 2008. ICED 2008. penang, pp. 1–6. Dec 2008

    Google Scholar 

  44. James, R., Shahana, T., Jacob, P., Sasi, S.: Fixed point decimal multiplication using RPS algorithm. In: IEEE International Symposium on Parallel and Distributed Processing with Applications 2008, Sydney, NSW, pp. 343–350 (2008)

    Google Scholar 

  45. Kaivani, A., Han, L., Ko, S.-B.: Improved design of high-frequency sequential decimal multipliers. Electron. Lett. Inst. Eng. Technol. 50(7), 558–560 (2014)

    Google Scholar 

  46. Kenney, R., Schulte, M., Erle, M.: A high-frequency decimal multiplier. In: Proceedings IEEE International Conference on Computer Design: VLSI in Computers and Processors, 2004. ICCD 2004, pp. 26–29 (2004)

    Google Scholar 

  47. Lin, K., Chiu, Y., Lin, T.-H.: A decimal squarer with efficient partial product generation. In: 18th IEEE/IFIP International Conference on VLSI and System-on-Chip 2010, Madrid, pp. 213–218 (2010)

    Google Scholar 

  48. Navarro, S., Tsen, C., Schulte, M.: Binary integer decimal-based floating-point multiplication. IEEE Trans. Comput. 62(7), 1460–1466 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  49. Ohtsuki, T., Oshima, Y., Ishikawa, S., Yabe, H., Fukuta, M.: Apparatus for decimal multiplication. US, Patent US 4677583 A, US. 30 June 1987

    Google Scholar 

  50. Osama, D., Khaleel, A., Tulic, N., Mhaidat, K.: FPGA implementation of binary coded decimal digit adders and multipliers. In: 8th International Symposium on Mechatronics and its Applications (ISMA), 2012, Sharjah, pp. 1–5 (2012)

    Google Scholar 

  51. Sutter, G., Todorovich, E., Bioul, G., Vazquez, M., Deschamps, J.: FPGA implementations of BCD multipliers. In: International Conference on Reconfigurable Computing and FPGAs, 2009. ReConFig ‘09. Quintana Roo, pp. 36–41 (2009)

    Google Scholar 

  52. Ueda, T.: Decimal multiplying assembly and multiply module. US, Patent US 5379245, US. Jan 1995

    Google Scholar 

  53. Vázquez, Á., Antelo, E., Bruguera, J.: Fast Radix-10 multiplication using redundant BCD codes. IEEE Trans. Comput. 63(8), 1902–1914 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  54. Veeramachaneni, S., Srinivas, M.: Novel high-speed architecture for 32-Bit binary coded decimal (BCD) multiplier. In: 2008 International Symposium on Communications and Information Technologies, 2008. ISCIT, Lao, pp. 543–546 (2008)

    Google Scholar 

  55. Véstias, M., Neto, H.: Iterative decimal multiplication using binary arithmetic. In: 2011 VII Southern Conference on VII Southern Conference on Programmable Logic (SPL). Cordoba, pp. 257–262 (2011)

    Google Scholar 

  56. Véstias, M., Neto, H.: Parallel decimal multipliers and squarers using Karatsuba-Ofman’s algorithm. In: 15th Euromicro Conference on Digital System Design (DSD), 2012, Izmir, pp. 782–788 (2012)

    Google Scholar 

  57. Véstias, M., Neto, H.: Parallel decimal multipliers using binary multipliers. In: VI Southern Programmable Logic Conference (SPL), 2010, Ipojuca, pp. 73–78 (2010)

    Google Scholar 

  58. Wahba, A., Fahmy, H.: Area efficient and fast combined binary/decimal floating point fused multiply add unit. IEEE Trans. Comput. (99), 1 (2016)

    Google Scholar 

  59. Zhu, M., Baker, A., Jiang, Y.: On a parallel decimal multiplier based on hybrid 8421–5421 BCD recoding. In: 2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS), Columbus, OH, pp. 1391–1394 (2013)

    Google Scholar 

  60. Zhu, M., Jiang, Y.: An area-time efficient architecture for 16 × 16 decimal multiplications. In: Tenth International Conference on Information Technology: New Generations (ITNG), 2013, Las Vegas, NV, pp. 210–216 (2013)

    Google Scholar 

  61. Baesler, M., Voigt, S.-O., Teufel, T.: A decimal floating-point accurate scalar product unit with a parallel fixed-point multiplier on a virtex-5 FPGA. Int. J. Reconfigurable Comput. 2010, 13 (2010). (Article ID 357839)

    Google Scholar 

  62. Cui, X., Liu, W., Wenwen, D., Lombardi, F.: A parallel decimal multiplier using hybrid binary coded decimal (BCD) codes. In: IEEE 23nd Symposium on Computer Arithmetic (ARITH) 2016 (2016)

    Google Scholar 

  63. Varma, C., Ahmed, S., Srinivas, M.: A decimal/binary multi-operand adder using a fast binary to decimal converter. In: 27th International Conference on VLSI Design and 2014 13th International Conference on Embedded Systems (2014)

    Google Scholar 

  64. Eduardo, C., Guardia, M.: Implementation of a fully pipelined BCD multiplier in FPGA. In: VIII Southern Conference on Programmable Logic (SPL) (2012)

    Google Scholar 

  65. Ding, H., Shu, P., Wang, X., Yang, J.: A design and implementation of decimal floating-point multiplication unit based on SOPC. In: Third International Conference on Digital Manufacturing and Automation (ICDMA) (2012)

    Google Scholar 

  66. Tsen, S., Gonzalez-Navarro, S., Schulte, M., Compton, K.: Hardware designs for binary integer decimal-based rounding. IEEE Trans. Comput. 60(5), 614–627 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  67. Vázquez, Á., Dinechin, F.: Efficient implementation of parallel BCD multiplication in LUT-6 FPGAs. In: International Conference on Field-Programmable Technology (FPT) (2010)

    Google Scholar 

  68. Navarro, S., Tsen, C., Schulte, M.: A binary integer decimal-based multiplier for decimal floating-point arithmetic. In: Forty-First Asilomar Conference on Signals, Systems and Computers, 2007. ACSSC 2007 (2007)

    Google Scholar 

  69. Rekha, K., Jacob, K., Sasi, S.: Performance analysis of double digit decimal multiplier on various FPGA logic families. In: 5th Southern Conference on Programmable Logic, 2009. SPL. Sao Carlos, pp. 165–170 (2009)

    Google Scholar 

  70. Minchola, C., Sutter, G.: A FPGA IEEE-754-2008 Decimal64 floating-point multiplier. In: International Conference on Reconfigurable Computing and FPGAs, 2009. ReConFig ‘09. Quintana Roo, pp. 59–64 (2009)

    Google Scholar 

  71. Kaivani, A., Chen, L., Ko, S.: High-frequency sequential decimal multipliers. In: 2012 IEEE International Symposium on Circuits and Systems (ISCAS). Seoul, pp. 3045–3048 (2012)

    Google Scholar 

  72. Lang, T., Nannarelli, A.: A Radix-10 combinational multiplier. In: Fortieth Asilomar Conference on Signals, Systems and Computers, 2006. ACSSC ‘06. Pacific Grove, CA, pp. 313–317 (2006)

    Google Scholar 

  73. Gorgin, S., Jaberipur, G., Parhami, B.: Design and evaluation of decimal array multipliers. In: 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers, pp. 1782–1786. IEEE. Nov 2009

    Google Scholar 

  74. Neto, H., Vestias, M.: Decimal multiplier on FPGA using embedded binary multipliers. In: 2008 International Conference on Field Programmable Logic and Applications, Heidelberg, pp. 197–202 (2008)

    Google Scholar 

  75. Gonzalez-Navarro, S., Tsen, C., Schulte, M.: A binary integer decimal-based multiplier for decimal floating-point arithmetic. In: 2007 Conference Record of the Forty-First Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, pp. 353–357 (2007)

    Google Scholar 

  76. Baesler, M., Voigt, S.-O., Teufel, T.: An IEEE 754-2008 decimal parallel and pipelined FPGA floating-point multiplier. In: 2010 International Conference on Field Programmable Logic and Applications (FPL). Milano, pp. 489–495 (2010)

    Google Scholar 

  77. Erle, M., Schwarz, E., Schulte, M.: Decimal multiplication with efficient partial product generation. In: 17th IEEE Symposium on Computer Arithmetic, 2005. ARITH-17 2005, pp. 21–28 (2005)

    Google Scholar 

  78. Jouppi, N.: Wallace-tree multipliers using half and full adders. US, Patent US 6065033 A, US. 16 May 2000

    Google Scholar 

  79. Lehman, M.: Short-cut multiplication and division in automatic binary digital computers, with special reference to a new multiplication process. Proc. IEEE—Part B: Radio Electron. Eng. 105(23), 496–504 (2010)

    Google Scholar 

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Correspondence to Diganta Sengupta .

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Sengupta, D., Sultana, M. (2018). Taxonomy of Decimal Multiplier Research. In: Das, S., Chaki, N. (eds) Algorithms and Applications . Smart Innovation, Systems and Technologies, vol 88. Springer, Singapore. https://doi.org/10.1007/978-981-10-8102-6_1

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