Probabilistic Error Analysis of Approximate Adders and Multipliers

  • Sana Mazahir
  • Muhammad Kamran Ayub
  • Osman Hasan
  • Muhammad Shafique


Approximate adders and multipliers are widely being advocated to be used in error resilient applications. A very important performance metric in this regard is the probability of occurrence of error in these arithmetic circuits as this allows us to choose the most efficient configuration of an adder or multiplier for a given application. In this chapter, we present an analytical error analysis approach for approximate adders, which comprise of subadder units, and recursive approximate multipliers with approximate partial products. We also derive probability mass function (PMF) of error for both of the considered adder and multiplier models. The results show that the proposed analysis serves as an effective tool for predicting, evaluating, and comparing the accuracy of various approximate adders and multipliers. For illustration purposes, we also show that the comparative performance of different approximate adders and multipliers can be correctly predicted in practical applications of image processing.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sana Mazahir
    • 1
  • Muhammad Kamran Ayub
    • 2
  • Osman Hasan
    • 2
  • Muhammad Shafique
    • 3
  1. 1.Georgia Institute of TechnologyAtlantaUSA
  2. 2.School of Electrical Engineering and Computer ScienceNational University of Sciences and Technology (NUST)IslamabadPakistan
  3. 3.Institute of Computer EngineeringVienna University of Technology (TU Wien)ViennaAustria

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