On Lookup Table Cascade-Based Realizations of Arbiters

This paper presents a new algorithm of iterative decomposition for multiple-output Boolean functions with an embedded heuristics to order variables. The algorithm produces a cascade of look-up tables (LUTs) that implements the given function and simultaneously a sub-optimal Multi-Terminal Binary Decision Diagram (MTBDD). The LUT cascade can be used for pipelined processing on FPGAs with BRAMs or at a non-traditional synthesis of large combinational and sequential circuits. On the other hand, suboptimal MTBBDs can serve as prototypes for efficient firmware implementation, especially when a micro-programmed controller that firmware runs on supports multi-way branching. A novel technique is illustrated on practical examples of three types of arbiters. It may be quite useful as a more flexible alternative implementation of digital systems with increased testability and improved manufacturability.