Skip to main content

Towards Area-Delay Efficient Reverse Conversion of Higher-Radix Signed-Digit Number Systems

  • Conference paper
  • First Online:
Advances in Electrical and Computer Technologies (ICAECT 2021)

Abstract

In spite of momentous attention received by the higher-radix signed-digit number systems, no significant work on the related reverse conversion has been reported yet. In this paper, it is shown that some minor pre-processing of higher-radix inputs may allow constituting the conversion control network for reverse conversion of higher-radix signed-digit number systems merely in terms of binary signed-digit number system. Subsequently several alternatives may become available for exploiting the reduced logical design at ease, considering various block factors at different levels of the conversion control network. As a case study, the 16-digit minimally redundant radix-4 signed-digit number system is investigated in this paper and on the basis of simulative study, the most potential candidate is determined for designing the convertor.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 279.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Koren I (2001) Computer arithmetic algorithms 2. CRC Press, London

    Google Scholar 

  2. Ercegovac MD, Lang T (2004) Digital arithmetic, 1st edn. Morgan Kaufmann Publishers (An Imprint of Elsevier), San Francisco

    Google Scholar 

  3. Armand A, Timarchi S (2019) Efficient error detection and correction method for 1-out-of-3 binary signed digit adders. Int J Electro 106:1427–1440

    Article  Google Scholar 

  4. Shah YA, Javeed K, Azmat S, Wang X (2019) Redundant-signed-digit-based high speed elliptic curve cryptographic processor. J Circuits Syst Comput 28:120–126

    Google Scholar 

  5. Chakraborty MS, Sao SK, Mondal AC (2018) Equivalence of reverse conversion of binary signed-digit number system and two’s-complement to canonical signed-digit recording. In: IEEE international conference on recent advances in information technology. Dhanbad pp 662–666

    Google Scholar 

  6. Kaivani A, Ko S (2016) Floating point butterfly architecture based on binary signed digit representation. IEEE Trans Very Large Scale Integr VLSI Syst 24:1208–1211

    Article  Google Scholar 

  7. Crookes D, Jiang M (2007) Using signed digit arithmetic for low power multiplication. Electron Lett 43:613–614

    Article  Google Scholar 

  8. Smitha KG, Fahmy AH, Vinod AP (2006) Redundant adders consume less energy. In: IEEE Asia Pacific conference on circuits and systems. Singapore pp 422–425

    Google Scholar 

  9. Juang T-B, Wei C-C, Chang C-H (2009) Area-saving technique for low-error redundant binary fixed-width multiplier implementation. In: IEEE international symposium on integrated circuits. Singapore pp 550–553

    Google Scholar 

  10. Jaberipur G, Ghodsi M (2003) High radix signed digit number systems: representation paradigms. Sci Iran 10:383–391

    MATH  Google Scholar 

  11. Sudan SS, Singhal M (2017) A review on basics of QSD number addition & subtraction. In: IEEE international conference on computing and communication technologies for smart nation. Gurgaon pp 13–17

    Google Scholar 

  12. Chakraborty MS (2020) Designing an on-line magnitude comparator for higher-radix. Int J Inf Tech Electr Eng 9:92–98

    Google Scholar 

  13. Chakraborty MS (2016) Reverse conversion schemes for signed-digit number systems: a survey. J Inst Eng (India): B 97:589–593

    Google Scholar 

  14. Charoensiri V, Surarerks A (2006) On-the-fly conversion from signed-digit number system into complement representation. In: IEEE international symposium on communications and information technologies. Bangkok pp 1056–1061

    Google Scholar 

  15. Parhami B (1990) Generalized signed-digit number systems: a unifying framework for redundant number representations. IEEE Trans Comput 39:89–98

    Article  Google Scholar 

  16. Avizienis A (1961) Signed-digit number representations for fast parallel arithmetic. IRE Trans Electron Comput EC-10 389–400

    Google Scholar 

  17. Tripathy SS, Barik RK, Pradhan M (2017) An improved conversion circuit for redundant binary to conventional binary representation. In: International conference on computational intelligence, communications and business analytics. Kolkata pp 363–371

    Google Scholar 

  18. He Y, Chang C-H (2008) A power-delay efficient hybrid carry-lookahead/carry-select based redundant binary to two’s-complement converter. IEEE Trans Circuits Syst I Regul Pap 55:336–346

    Google Scholar 

  19. Sahoo SK, Gupta A, Asati AR, Shekhar C (2010) A novel redundant binary number to natural binary number converter. J Signal Process Syst 59:297–307

    Article  Google Scholar 

  20. Srikanthan T, Lam SK, Suman M (2004) Area-time efficient sign-detection technique for binary signed-digit number system. IEEE Trans Comput 53:69–72

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Madhu Sudan Chakraborty .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Chakraborty, M.S., Sreelakshmi, G., Chakraborty, A., Sao, S.K., Sahana, D.C. (2022). Towards Area-Delay Efficient Reverse Conversion of Higher-Radix Signed-Digit Number Systems. In: Sengodan, T., Murugappan, M., Misra, S. (eds) Advances in Electrical and Computer Technologies. ICAECT 2021. Lecture Notes in Electrical Engineering, vol 881. Springer, Singapore. https://doi.org/10.1007/978-981-19-1111-8_1

Download citation

  • DOI: https://doi.org/10.1007/978-981-19-1111-8_1

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-1110-1

  • Online ISBN: 978-981-19-1111-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics