Reversible Logic Based Design and Test of Field Coupled Nanocomputing Circuits - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 132

missing/additional cell defect in the QCA layout of the Fredkin gate.
We are also presenting a new conservative logic gate called Multiplexer
Conservative QCA gate (MX-cqca) that is not reversible in nature but
has similar properties as the Fredkin gate of working as 2:1 multiplexer.
The proposed MX-cqca gate surpasses the Fredkin gate in terms of com-
plexity (the number of majority voter), speed and area.

· ·

Keywords: Conservative logic Reversible logic Quantum dot cellular

automata

1 Introduction

Reversible logic has applications in emerging technologies such as quantum com-
puting, quantum dot cellular automata, optical computing, etc [ 37 , 38 , 44 , 47 , 63 ].
Reversible logic based circuits satisfy the property that there is one-to-one map-
ping between the input and the output vectors, that is for each input vector
there is a unique output vector and vice-versa. Conservative logic is a logic fam-
ily which exhibit the property that there are equal number of 1s in the outputs
as in the inputs. Conservative logic may or may not be in reversible in nature.
Conservative logic is called reversible conservative logic when there is a one-to-
one mapping between the input and the output vectors along with the property
that there are equal number of 1s in the outputs as in the inputs. Conservative
logic circuits are not considered reversible, if one-to-one mapping between the
input and the output vectors is not preserved.
Researchers have proved that if the computation is performed in a irreversible
manner each bit of information lost will produce kT ln2 Joules of heat energy [ 31 ].
From thermodynamic point of view, in order to avoid this limit, Bennett showed
that kT ln2 energy dissipation would not occur, if a computation is carried out in
a reversible way [ 5 ]. Thus, from thermodynamic considerations, a firm lower limit
on dissipation of

18 meV (in room-temperature environment)
is a necessity for conventional (irreversible) logic, even if reliability issues could
be ignored. Reversible logic can be useful to design non-dissipative circuits if the
physical implementation of the logic is also physically reversible. CMOS cannot
be considered as a practical implementation platform as CMOS is not physically
reversible. In modern CMOS technology, voltage-coded logic signals have an
energy of

E diss = kT ln2 ≈

2 , and whenever the node voltage is changed, it leads
to dissipation of this energy and is order of magnitude higher than the kT ln2
factor. In contrast, there are emerging nanotechnologies such as Quantum Dot
Cellular automata (QCA) computing, Optical Computing, and Superconductor
Flux Logic (SFL) family, etc., where the energy dissipated due to information
destruction will be a significant factor of the overall heat dissipation of the
system [ 4 , 13 , 19 , 30 , 55 , 56 , 58 ]. Thus, one of the primary motivations for adopting
reversible logic lies in the fact that it can provide a logic design methodology
for designing ultra-low power circuits beyond kT ln2 limit for those emerging
nanotechnologies in which the energy dissipated due to information destruction

E sig =(1 / 2) CV