Design procedures and NML cost analysis of reversible barrel shifters optimizing garbage and ancilla lines

Abstract

Reversible computing generates a unique output from each input and vice versa. In addition, conservative reversible logic is useful to design ultra-low-power nanocomputing circuits, circuits for quantum computing, and nanocircuits that are testable in nature. Reversible computing circuits require ancilla inputs and garbage outputs to maintain reversibility. An ancilla input is the constant input in a reversible circuit. A garbage output is an output which exists in the circuit just to maintain one-to-one mapping but is not a primary nor a useful output. An efficient reversible circuit will have a minimal number of garbage and ancilla bits. Furthermore, the barrel shifter is one of the main computing systems having applications in high-speed digital signal processing, floating-point arithmetic, field programmable gate arrays, and central processing units. A barrel shifter can shift and rotate multiple bits in a single clock cycle. In this work, we proposed five designs of barrel shifters based on reversible computing that are optimized in terms of the number of garbage outputs and the number of ancilla inputs. To achieve this goal, a new super conservative reversible logic gate (SCRL gate) has been proposed. The SCRL gate has 1 control input depending on the value of which it can swap any two $$n-1$$n-1 data inputs. The five proposed designs consist of reversible right rotator, reversible logical right shifter, reversible arithmetic right shifter, reversible universal right shifter, and reversible universal bidirectional shifter. The proposed designs of reversible barrel shifters are compared with the existing works in the literature and have shown improvements ranging from 8.57 to 91.62 % in terms of the number of ancilla inputs and from 17.72 to 91.62 % in terms of the number of garbage outputs. A cost analysis was made for their potential implementation in nanomagnetic logic (NML) computing. It is illustrated that the SCRL gate-based designs of reversible barrel shifters have less NML cost (cost in terms of number of inverters and majority voters) compared to the Fredkin gate-based designs of reversible barrel shifters.