Garbage-Free Reversible Integer Multiplication with Constants of the Form 2k±2l±1

  • Holger Bock Axelsen
  • Michael Kirkedal Thomsen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7581)


Multiplication of integers is non-injective and, thus, requires garbage lines for any reversible logic implementation. However, multiplying with a fixed constant is injective, and should therefore be implementable in reversible logic without garbage. Despite this, the only reported circuits for constant multiplication without garbage are restricted to powers of 2, i.e., the multiplication is a simple bit-shift.

Here, we show how to generate a garbage-free linear-depth reversible logic circuit for multiplying an input integer with a constant of the form 2 k ±1 or 2 k ±2 l ±1, by building on a simple strength reduction to addition. Using several such circuits in sequence allows us to support a greater variety of constants. This enables wider use of constant multiplication in garbage-free reversible circuits than was previously possible.


Reversible circuits logic design constant multipliers garbage-free 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Holger Bock Axelsen
    • 1
  • Michael Kirkedal Thomsen
    • 1
  1. 1.DIKU, Department of Computer ScienceUniversity of CopenhagenDenmark

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