Reversible Logic Gates

  • Kenichi Morita
Part of the Monographs in Theoretical Computer Science. An EATCS Series book series (EATCS)


A reversible logic gate is a memory-less logic element that realizes an injective logical function. Fredkin gate, Toffoli gate, interaction gate, and switch gate are typical ones. Here, we investigate basic properties of reversible logic gates and circuits, which are needed in the following chapters. First, logical universality of them is discussed. Then, a construction method of an almost garbage-less reversible combinatorial logic circuit is explained. Reducing the total amount of garbage signals is an important problem in designing reversible logic circuits. Finally, relations among Fredkin gate, reversible logic elements with 1-bit memory (RLEMs), and reversible sequential machines (RSM) are studied. In particular, it is shown that we can construct a completely garbage-less circuit out of Fredkin gates and delay elements that simulates a given RSM. This result will be used to show universality of reversible cellular automata in the later chapters.


reversible logic gate Fredkin gate garbage-less circuit rotary element reversible sequential machine 


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Copyright information

© Springer Japan KK 2017

Authors and Affiliations

  • Kenichi Morita
    • 1
  1. 1.Professor Emeritus, Hiroshima UniversityHiroshimaJapan

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