This document discusses reversible logic synthesis methodologies. It begins by defining reversible logic circuits as those that do not lose information and have one-to-one input-output mappings. There are constraints against feedback and fan-out in reversible logic synthesis. Methods for reversible logic synthesis include reversible decision trees, diagrams, lattice circuits, group-theoretic representations, and cascade circuits. The document evaluates seven main synthesis methods and finds that reversible cascade circuits and group-theoretic representations generally produce the lowest gate counts and garbage outputs.

1. REVERSIBLE LOGIC
SYNTHESIS
METHODOLOGIES
Done by
Yousif Hazem Jasim

2. CONTENTS
1-Reversible Logic Circuits
2-Reversible Logic Gates
3-Reversible Logic Synthesis
4-comparative between Reversible logic synthesis
methods
5-conclusion

3. Reversible logic circuits are those circuits that do not lose information. Reversible logic
circuits have the same number of inputs and outputs, and have one-to-one mappings between
vectors of inputs and outputs; thus the vector of inputs states can be always reconstructed
from the vector of output states.
Two constraints for reversible logic synthesis are:
1. Feedback is not allowed.
2. Fan-out is not allowed.
For an (n, k) function, i.e. function with n-input k-output, it is necessary to add inputs and/or
outputs to make it reversible. This leads to the following definition.
Definition “Garbage” is the number of outputs added to make an (n,k) function reversible.
the word "constant inputs" is used to denote the preset values inputs that were added to an
(n, k) function to make it reversible.
The relation between garbage outputs and constant inputs is .
Input + constant input = output + garbage
1- Reversible Logic Circuits

4. 2-Toffoli Gate
1-Feynman Gate 3-Fredkin Gate
2-Reversible Logic
Gates

5. 1-Reversible Decision
Trees
3-Methods of Reversible Logic Synthesis
Example: F = ab + bc + ac

6. 2-Reversible Decision
Diagram

7. A-Synthesis stage B-Analysis stage
3-Reversible Lattice Circuits

8. 4-Group-Theoretic
Representation
5-Reversible Programmable Gate
Array

9. 6-Reversible cascade Circuits 7-Transformation-Based Network
Synthesis of Fredkin-Toffoli Gates
Results of applying the 7 synthesis methods to the Boolean function f

10. 4-comarative between Reversible Logic Synthesis methods

12. There are 12 methods of reversible logic synthesis, we work on the
seven methods which are the most widely used of the design of
reversible logic circuits, in our work we found that the most desirable
one is the Reversible Cascade Circuits and the Group - Theoretic
Representations which produce the lowest number of gates as well as
the lowest number of garbage as mentioned in table 3.2& 3.3, in order
to figure out which method is the most reliable we made a comparison
on the advantages and disadvantages between the seven methods as
mentioned in table 2.4. In the reversible cascade method, it was found
that this method does not produce any garbage with only 3 gates table
3.2, and producing 1 garbage and 3 gates table 3.3, and the group
theoretic representation producing 2 garbage's and 2 gates table 3.2 and
3.3. In the end we figured out that the reversible cascade circuits
method is the one that we can rely on in the design of the reversible
logic circuits because it does not produce any garbage on average and
Good for multi-output functions.
5-conclusions

13. Thank you