Arbitration between various contenders using given priority parameters is difficult to implement in hardware. We present a solution that solves this problem with minimal hardware. The solution presented is simple, fair, starvation-free, and fast. A contention resolving technique, called binary tree arbitration, is taken as a basis for implementing a "weighted fair" contention resolution technique that picks among "n" contenders, which could translate to flows, packets/cells, or connections. The extensions are priority and embedded binary tree arbitrations. Theoretical formulations of these techniques are presented. The results of their comparisons to software and hardware simulations, to show their relative conformance, are also presented.