Matthew Morrison, Student Member, IEEE, Matthew Lewandowski, Student Member, IEEE, and Nagarajan
Ranganathan, Fellow, IEEE
Abstract—Programmable reversible logic is gain wide
consideration as a logic design style for modern nanotechnology
and quantum computing with minimal impact on circuit heat
generation in improved computer architecture and arithmetic
logic unit designs. In this paper, a 2*2 Swap gate which is a
reduced implementation in terms of quantum cost and delay to
the previous Swap gate is presented. Then, a novel 3*3
programmable UPG gate capable of calculating the
universal logic calculations is presented and verified, and
its advantages over the Toffoli and Peres gates are
discussed. The UPG is then implemented in a reduced
design for calculating n-bit AND, n-bit OR and n-bit
ZERO calculations. Then, two 3*3 RMUX gates capable
of multiplexing two input values with reduced quantum
cost and delay compared to the previously existing
Fredkin gate is presented and verified. Next, a novel 4*4
reversible programmable RC gate capable of nine unique
logical calculations at low cost and delay is presented and
verified. The UPG and RC are implemented in the design
of novel sequential and tree-based comparators. These
designs are compared to previously existing designs, and
their advantages in terms of cost and delay are analyzed.
Then, the RMUX is used to improve a reversible SRAM
cell we previously presented. The memory cell and
comparator are implemented in the design of a Min/Max
Comparator device.
Index Terms – Comparator; Emerging Technologies; Low
Power; Microprocessor; Multiplexer; Reversible Logic; Static
RAM
I. INTRODUCTION
EVERSIBLE logic is a computing design standard where
the ideal implementation would produce zero entropy
gain [1][13][14][17]. Any reversible logic structure requires
an identical number of input and output lines, and is bijective
in nature. The three major design goals of reversible logic are
as follows. First, minimization of the quantum cost - the
number of 1*1 and 2*2 reversible calculations necessary to
generate the logical output - will reduce the device’s
computational complexity. Second, minimization of the delay
- the logical depth of the device – will improve the throughput
of the device. Third, reduction of the ancillary inputs and
garbage outputs - inputs and outputs not implemented in the
design of the gate and only serve to maintain reversibility of
the device – will improve the design space require to
implement the logic.
In Section II, a novel 3*3 programmable UPG gate is
proposed and verified that may be utilized in a design
requiring a low-cost reversible calculation of AND, NAND,
OR, NOR. Next, a novel 5*5 RC gate is presented and
verified which may be implemented in an ALU for the
calculation of nine logical calculations, and also may be
implemented in the design of a comparator. In Section III, the
UPG and RC are implemented in the design of novel
sequential and tree-based comparators. The designs are
verified, and are compared to reversible comparators
previously existing in the literature. The advantages of the
proposed designs are analyzed in terms of quantum cost and
delay. In Section IV, the RMUX is used to improve a
reversible SRAM cell we previously presented. The proposed
design is verified and compared to the previous design in
terms of quantum cost and delay. In Section V, the memory
cell and comparator are implemented in the design of a
Min/Max Comparator device.
II. NOVEL REVERSIBLE LOGIC GATES
A. Proposed Swap Gate
We propose a reduced implementation of the reversible
Swap Gate, which is designed using two integrated qubit
gates, and produces a swap of the two input values on the
output gate. Previously, the swap gate was implemented using
three Feynman gates which produced the outputs
and , which produces
the swap, and incurred a quantum cost and delay of 3. The
proposed implementation is accomplished with a quantum
cost and delay of 2, was verified using VHDL in Xilinx ISE
12.4, and is shown in Fig. 1.
Fig 1: Integrated Qubit Gates Implemented as a Swap Gate
Design of a Tree-Based Comparator and
Memory Unit Based on a Novel Reversible
Logic Structure
R
2012 IEEE Computer Society Annual Symposium on VLSI
978-0-7695-4767-1/12 $26.00 © 2012 IEEE
DOI 10.1109/ISVLSI.2012.61
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