Abstract: A traditional bottom-up modeling method for minimum configuration numbers is adopted for the study of FPGA minimum configurations. This method is limited if a large number of LUTs and multiplexers are presented. Since graph theory has been extensively applied to circuit analysis and test, this paper focuses on the modeling FPGA configurations. In our study, an internal logic block and interconnections of an FPGA are considered as a vertex and an edge connecting two vertices in the graph, respectively. A top-down modeling method is proposed in the paper to achieve minimum configuration numbers for CLB and IOB. Based on the proposed modeling approach and exhaustive analysis, the minimum configuration numbers for CLB and IOB are five and three, respectively.

Key words: graph theory, minimum configuration number, FPGA, CLB, IOB