A Systematic Approach for Arbitration Expressions

Greedy arbiters and bundling merges compose simultaneous events in sequence and parallel respectively. Previous designs for these problems handle two to three inputs, and can be composed in a tree topology to handle more. In addition, they include subtle timing assumptions beyond the QDI delay model and undocumented timing assumptions in their arbiter's digital model. In this article, we discuss two slightly different digital models that we call the ideal arbiter and buffered arbiter models, and match them to CMOS implementations. From CHP specifications of the greedy arbiter and bundling merge, we derive the Maybe Execute Element. We then show how it may be systematically composed to produce improved circuits for both which use a small number of simple gates, strictly abide by the QDI delay model, and gracefully scale to an arbitrary number of inputs. Finally, we touch on how this approach may be used to develop scalable circuit solutions to more sophisticated arbitration problems.