Efficient parity prediction in FPGA

We propose, in this paper, XOR-based decomposition methods to implement parity prediction circuits efficiently in field programmable gate arrays (FPGAs). The first proposed method is an extension of the Shannon's expansion theorem. Such extension enables us to force decomposing the parity prediction circuit into appropriate size sub-circuits. The second proposed method is based on the Reed-Muller canonical form that transforms AND/OR Boolean functions to AND/XOR functions. The XOR relation enables us to find more efficient grouping for the parity prediction function. The MCNC benchmark circuits are used to demonstrate the effectiveness of the proposed techniques.