Minimization of Permuted Reed-Muller Trees and Reed-Muller Trees for Cellular Logic Programmable Gate Arrays

• Main Author: Wu, Lifei
• Format: Others
• Published: PDXScholar 1993
• Subjects: Gate array circuits; Programmable logic devices; Computer algorithms; Electrical and Computer Engineering
• Online Access: https://pdxscholar.library.pdx.edu/open_access_etds/4745; https://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=5816&context=open_access_etds

The new family of Field Programmable Gate Arrays, CLI 6000 from Concurrent Logic Inc realizes truly Cellular Logic. It has been mainly designed for the realization of data path architectures. However, the realizable logic functions provided by its macrocells and their limited connectivity call also for new general-purpose logic synthesis methods. The basic cell of CLi 6000 can be programmed to realize a two-input multiplexer ( A*B + C*B ), an AND/EXOR cell ( A*B Ea C ), or the basic 2-input AND, OR and EXOR gate. This suggests to using these cells for tree-like expansions. These "cellular logic" devices require regular connection patterns in the netlists resulting from logic synthesis. This thesis presents a synthesis tree searching program PROMPT, which generates AND/EXOR tree circuits from given Boolean functions. Such circuits have the property that the gate structures are AND/EXOR ( A *B EB C ), AND and EXOR which could be realized by the CLI6000 cells. Also, the connection. way in the circuit is that usually the output of one level gate is the input of the next level gate of the tree. This matches ideally to the architecture of the CLI6000 bussing network where the macrocells have only connections to their neighboring cells. PROMPT is based on the Davio expansions ( an equivalent of the Shannon expansions for the EXOR gates ) as its Boolean decomposition methods. The program includes three versions: exact version, heuristic version and fixed-variable version. The exact version of PROMPT generates the Permuted Reed-Muller Tree circuit which has the minimum number of gates. Such tree circuit is obtained by searching through all possible combinations of the expansion variable orders to get the one which needs the least number of gates. The heuristic version of PROMPT is designed to decrease the time complexity of the search algorithm when dealing with logic functions having many input variables. It generates a Permuted Reed-Muller Tree which may not have the minimum number of gates. However, the tree searching time in this version decreases tremendously compared to the time necessary in the exact version. The fix-variable version is developed to generate Reed-Muller Tree circuits. Such circuits will have the same expansion variables at the same tree level, so they can be easier routed after the placement to the CLI6000 chips. In short, the program PROMPT generates the PRM and RM tree circuits which are particularly well matched to both the realization of logic cell and connection structure of the CLI6000 device. Thus, the PRM and RM circuits can be easily placed and routed on the CLI6000 FPGAs.