Design Methodologies for Reversible Logic Based Barrel Shifters

Abstract

Barrel shifter is an integral component of processor datapaths in computing systems since it can shift and rotate multiple bits in a single cycle. Furthermore, reversible logic has applications in emerging computing paradigms such as quantum computing, quantum dot cellular automata, optical computing, etc. In this work, we propose efficient methodologies for designing reversible barrel shifters. The proposed methodologies are designed using Fredkin gate and Feynman gate (FG). The Fredkin gate is used because it can implement a 2:1 MUX with minimum quantum cost, minimum number of ancilla inputs and garbage outputs, and the Feynman gate is used to avoid a fanout since a fanout is not allowed in reversible logic. In the existing literature, design methodologies are limited to the design of a ([Formula: see text]) reversible left rotator that can only perform the left rotate operation. This work explores the other primary functionalities of a reversible barrel shifter such as the design of a reversible: (i) logical right shifter, (ii) universal right shifter that supports logical right shifter, arithmetic right shifter and right rotate operation, (iii) bidirectional logical shifter and (iv) universal bidirectional shifter that supports bidirectional logical and arithmetic shifter and rotate operations. The other types of reversible barrel shifters can also be easily designed by making minor modifications in the proposed methodologies. The proposed design methodologies are generic in nature and can be implemented using any barrel shifter of ([Formula: see text]) size, where n and k are the number of data bits and shift value, respectively. In order to minimize the number of ancilla inputs and garbage outputs, strategies such as the implementation of an n number of 2:1 MUXes as a chain of n Fredkin gates and the mapping of the two different 2:1 MUXes that are controlled by a common control signal but having the swapped controlled signals on a single Fredkin gate, are utilized. The design methodologies are evaluated in terms of the number of garbage outputs, the number of ancilla inputs and quantum cost. For a ([Formula: see text]) reversible barrel shifter, the relations between the varying values of n and k and their impact on the number of garbage outputs, the number of ancilla inputs and quantum cost are also established to help the designers in choosing an efficient barrel shifter according to their design needs.