In biology, Boolean networks are conventionally used to represent and simulate gene regulatory networks. The attractors are the subject of special attention in analyzing the dynamics of a Boolean network. They correspond to stable states and stable cycles, which play a crucial role in biological systems. In this work, we study a new representation of the dynamics of Boolean networks that are based on a new semantics used in answer set programming (ASP). Our work is based on the enumeration of all the attractors of asynchronous Boolean networks having interaction graphs which are circuits. We show that the used semantics allows to design a new approach for computing exhaustively both the stable cycles and the stable states of such networks. The enumeration of all the attractors and the distinction between both types of attractors is a significant step to better understand some critical aspects of biology. We applied and evaluated the proposed approach on randomly generated Boolean networks and the obtained results highlight the benefits of this approach, and match with some conjectured results in biology.