This paper is on broadcast and agreement in asynchronous message-passing systems made up of n processes, and where up to t processes may have a Byzantine Behavior. Its first contribution is a powerful , yet simple, all-to-all broadcast communication abstraction suited to binary values. This abstraction, which copes with up to t < n/3 Byzantine processes, allows each process to broadcast a binary value, and obtain a set of values such that (1) no value broadcast only by Byzantine processes can belong to the set of a correct process, and (2) if the set obtained by a correct process contains a single value v, then the set obtained by any correct process contains v. The second contribution of the paper is a new round-based asynchronous consensus algorithm that copes with up to t < n/3 Byzantine processes. This algorithm is based on the previous binary broadcast abstraction and a weak common coin. In addition of being signature-free and optimal with respect to the value of t, this consensus algorithm has several noteworthy properties: the expected number of rounds to decide is constant; each round is composed of a constant number of communication steps and involves O(n²) messages; each message is composed of a round number plus a constant number of bits. Moreover , the algorithm tolerates message reordering by the adversary (i.e., the Byzantine processes).