Fpga hw accelerator of the first step of systematic two-level minimization of single-output boolean function

Abstract

Boolean function minimization is an area important not only in the development and optimization of digital logic, but also in other research and development areas, such as, the optimization of control systems, simplifying program logic, artificial intelligence, etc. The aim of this paper is to present a hardware accelerated first step of the systematic minimization of single-output Boolean functions – the generation of a set of prime implicants for both the disjunctive normal form (DNF) and the conjunctive normal form (CNF), having defined the OFF and ON sets and – alternatively – also the DC (“don't care”) set. The proposed hardware accelerator is designed as combinational logic, described in VHDL. Its advantages include an extremely short prime-implicant-generation time in the order of ns and/or tens of ns – in case of Boolean functions with small amount of input variables – and the possibility to generate the valid-prime-implicant set of Boolean functions having a defined number of input variables at a constant time, regardless of the cardinality of the ON or, eventually, the DC sets. However, these advantages come with a large spatial complexity – the number of utilized implementation elements – of the respective combinational module, generating the prime-implicant set. The authors verified the proposed design using Field Programmable Gate Array (FPGA) technology, implementing the hardware using a Xilinx Kintex-7 KC-705 Evaluation Kit development board.