We introduce a non-blocking full/empty bit primitive, or NB-FEB for short, as a promising synchronization primitive for parallel programming on manycore architectures. We show that the NB-FEB primitive is universal, scalable, feasible and easy to use. NB-FEB, together with registers, can solve the consensus problem for an arbitrary number of processes (universality). NB-FEB is combinable, namely its memory requests to the same memory location can be combined into only one memory request, which consequently makes NB-FEB scalable (scalability). Since NB-FEB is a variant of the original full/empty bit that always returns a value instead of waiting for a conditional flag, it is as feasible as the original full/empty bit, which has been implemented in many computer systems (feasibility). We construct, on top of NB-FEB, a non-blocking software transactional memory system called NBFEB-STM, which can be used as an abstraction to handle concurrent threads easily. NBFEB-STM is space efficient: the space complexity of each object updated by N concurrent threads/transactions is Q(N){\it \Theta}(N), which is optimal.