Exploiting Reversible Computing for Latent-Fault-Free Error Detecting/Correcting CMOS Circuits

Abstract

Unlike conventional CMOS circuits, reversible circuits do not have latent faults, so faults occurring in internal circuit nodes always result in an error at the output. This is a unique feature for online or concurrent fault tolerance and the main motivation of this paper with an aim of achieving highly efficient fault-tolerant CMOS logic circuits. For this purpose, we first implement fault-tolerant reversible circuits. We develop two techniques to make a reversible circuit fault-tolerant by using multiple-control Toffoli gates. The first technique is based on single parity preserving and offers error detection for odd number of errors at the output. The second technique is constructed on Hamming codes, which results in circuits detecting any number of errors unless the number of errors at the output is the order of $d$ or correcting $(d-1)/2$ bit errors, where $d$ is the minimum Hamming distance between any pair of bit patterns. We select $d=3$ in this paper. We also claim that 100% error detection is possible with conservative reversible gates, such as a Fredkin gate. For this purpose, we develop a greedy synthesis algorithm that implements an arbitrary reversible function with multiple-control Fredkin gates. As the next step, we utilize the proposed reversible circuits with conventional CMOS gates. This certainly approves the practical use of the proposed techniques. The effectiveness of our techniques is demonstrated on benchmark circuits, implemented by both reversible and CMOS gates, in terms of fault tolerance performances and area costs. Comparisons with the related studies in the literature as well as with dual-modular redundancy and triple-modular redundancy-based circuits clearly favor the proposed designs.