Reversible Logic: A Decomposition using Reversible Gates - Perkowski et al., 2001, Slides of Computer Science

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A General Decomposition

for Reversible Logic

M. Perkowski, L. Jozwiak#, P. Kerntopf+, A. Mishchenko, A. Al-Rabadi, A. Coppola@, A. Buller, X. Song, M. Md. Mozammel Huq Azad Khan&, S. Yanushkevich^, V.Shmerko^, M. Chrzanowska-Jeske*

Portland State University, Portland, Oregon 97207- #Technical University o f Eindhoven, Eindhoven, The Netherlands, + Technical University of Warsaw, Warsaw, Poland, @ Cypress Semiconductor Northwest and Oregon Graduate Institute, Oregon, USA , * Information Sciences Division, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan, & Department of Computer Science and Engineering, East West University, Bangladesh, , ^ Technical University of Szczecin, Szczecin, Poland

Year

• Plot showing the number of dopant impurities involved in logic with bipolar transistors with year. - (Copyright 1988 by International Business Machines

Corporation, reprinted with permission.)

R. W. Keyes, IBM J. Res. Develop. 32 , 24 (1988).

Computing at the atomic scale:

a survey made by Keyes in 1988

Information loss = energy loss

• The loss of information is associated with laws of physics requiring that one bit of information lost dissipates k T ln 2 of energy, where k is Boltzmann’ constant and T is the temperature of the system.
• Interest in reversible computation arises from the desire to reduce heat dissipation , thereby allowing: - higher densities - speed

R. Landauer, “Fundamental Physical Limitations of

the Computational Process”, Ann. N.Y. Acad.Sci, 426, 162(1985). Docsity.com

Reversible Logic

• Bennett showed that for power

not be dissipated in the circuit it is necessary that arbitrary circuit can be build from reversible gates.

Information is Physical

• Is a minimum amount of energy required per computation step? - Rolf Landauer, 1970. Whenever we use a logically

irreversible gate we dissipate energy into the

environment.

A

B A^ ⊕^ B

A

B

A

reversible A ⊕ B

Reversible computation:

• Landauer/Bennett: almost all operations required in

computation could be performed in a reversible manner,

thus dissipating no heat!

• The first condition for any deterministic device to be

reversible is that its input and output be uniquely retrievable

from each other.

• This is called logical reversibility.
• The second condition: a device can actually run

backwards then it is called physically reversible

• and the second law of thermodynamics guarantees that it dissipates no heat.

Billiard Ball Model Docsity.com

Reversible logic

Reversible are circuits (gates) that have one- to-one mapping between vectors of inputs and outputs; thus the vector of input states can be always reconstructed from the vector of output states.

INPUTS OUTPUTS

Reversible logic constraints

Feedback not allowed in

combinational part

Fan-out not allowed

In some papers allowed under certain conditions

In some papers allowed in a limited way in a “near reversible” circuit

• To understand reversible

logic, it is useful to have intuitive feeling of various models of its realization.

Definitions

• A gate with k inputs and k outputs is called a _kk_* gate.
• A conservative circuit preserves the number of logic values in all combinations.
• In balanced binary logic the circuit has half of minterms with value 1.

Billiard Ball Model

DEFLECTION

SHIFT

DELAY

• This is described in E. Fredkin and T. Toffoli, “Conservative Logic”, Int. J.Theor. Phys. 21, (1982). Docsity.com

Interaction gate Input output A B z1^ z2 z3 z 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1

A Z1= A and B

B (^) Z4 = A and B

Z2 = B and NOT A Z3 = A and NOT B

A

B

Z1= A and B Z2 = B and NOT A Z3 = A and NOT B

Z4 = A and B

Inverse Interaction gate input output z1 z2 z3 z4 A B 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1

A Z1= A and B

B (^) Z4 = A and B

Z2 = B and NOT A Z3 = A and NOT B

Other input combinations not allowed

z z z z

A

B

Designing with this types of gates is difficult Docsity.com