Abstract
In this work, a novel quaternary algebra has been employed to design quaternary encoders and decoders of any size. Both priority and ordinary encoders has been designed. The priority encoder in this work may have any arbitrary permutation of input priorities; the design procedure is generic and works for any such permutation. Although no work has ever been done regarding arbitrarily large and randomly prioritized priority encoders in quaternary domain, there exist numerous reports on smaller encoders as well as decoders. The design complexity of the present work has been compared with some of such works done earlier and our designs are more favorable in terms of complexity, especially for large encoders and decoders.